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The  Microscopy  of  Drinking  Water. 

Third  Edition,  Rewritten  and  Enlarged. 

With  a  Chapter  on  the  Use  of  the  Microscope,  by  John 

W.  M.  Bunker,  Ph.D. 

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Vital  Statistics. 

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BY  HENRY  BALDWIN  WARD 

AND 

GEORGE  CHANDLER  WHIPPLE 

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Fresh- Water  Biology. 

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VITAL  STATISTICS 

AN  INTRODUCTION  TO  THE  SCIENCE 
OF  DEMOGRAPHY 


BY 

GEORGE  CHANDLER  WHIPPLE 

Professor  of  Sanitary  Engineering  in  Harvard  University 

Member  of  the  Public  Health  Council,  Massachusetts 

State  Department  of  Health 


FIRST  EDITION 


NEW  YORK 
JOHN  WILEY  &  SONS,  INC. 

LONDON:  CHAPMAN  &  HALL,   LIMITED 
1919 


COPYRIGHT,  1919, 

BY 
GEORGE  CHANDLER  WHIFFLE 


Stanhope 

F.    H.GILSON   COMPANY 
BOSTON,  U.S.A. 


DEDICATED  TO 

THE    STUDENTS    OF    VITAL    STATISTICS 

IN   THE   SCHOOL   OF   PUBLIC   HEALTH 

OF      HARVARD   UNIVERSITY 

AND   THE 
MASSACHUSETTS   INSTITUTE   OF   TECHNOLOGY 


PREFACE 

This  book  is  written  for  students  who  are  preparing  them- 
selves to  be  public  health  officials  and  for  public  health 
officials  who  are  willing  to  be  students.  It  makes  no  claim 
to  be  an  exhaustive  treatise  or  a  compendium  of  facts; 
it  is  merely  a  guide  to  the  study  of  vital  statistics,  an 
introduction  to  the  great  world-wide  science  of  demogra- 
phy —  a  science  yet  in  the  magmatic  stage,  not  yet  crystal- 
lized. The  Great  War  is  bound  to  develop  this  science, 
because  hereafter  all  the  nations  of  the  earth  must  know  each 
other  better,  and  this  knowledge,  in  order  to  be  usable,  must 
be  condensed  into  statistical  forms. 

Specifically  the  book  tells  what  statistics  are  and  what 
they  are  not;  it  shows  how  to  express  vital  facts  by  figures, 
how  to  tabulate  them  and  how  to  display  them  by  diagrams; 
it  shows  how  to  compute  birth-rates  and  death-rates  and 
how  to  analyze  a  death-rate;  it  shows  how  to  adjust  and 
standardize  death-rates  and  how  to  make  life  tables;  it  em- 
phasizes the  need  of  using  vital  statistics  with  truth,  with 
imagination  and  with  power.  • 

For  the  convenience  of  school  instruction,  exercises  and 
questions  to  incite  further  study  are  given  in  each  chapter. 
Many  subjects  worthy  of  special  study,  however,  are  not 
even  mentioned,  loose  ends  have  been  left  in  every  chapter, 
illustrations  have  been  chosen  as  they  came  conveniently  to 
hand,  and  the  general  arrangement  has  been  informal  as  to  its 
subject  matter.  The  object  in  all  this  has  been  to  stimulate 
the  reader  to  critically  analyze  all  vital  statistics  as  they  ap- 
pear before  him  from  day  to  day.  Although  the  illustrations 
have  been  gathered  in  a  haphazard  way,  an  attempt  has  been 
made  to  set  forth  the  elementary  principles  of  the  statistical 
method  in  a  simple  and  orderly  fashion. 


yi  PREFACE 

The  author  wishes  to  confess  that  he  is  not  an  authority 
on  vital  statistics,  much  less  an  authority  on  demography; 
he  is  merely  a  student  of  the  science.  He  has  taken  the 
student's  privilege  of  quoting  freely  from  many  writers  to 
whom  he  wishes  to  render  acknowledgments  and  thanks. 
In  particular  he  desires  to  express  his  obligations  and  personal 
regards  to  Dr.  William  H.  Davis,  Chief  Statistician  for  Vital 
Statistics,  United  States  Bureau  of  the  Census,  who  has  read 
the  entire  proof  of  this  book  and  given  the  benefit  of  his 
careful  criticism. 

Just  a  personal  word  to  the  health  officers  of  America. 
A  new  day  is  dawning  for  you.  The  care  of  the  public 
health  is  becoming  a  distinct  profession.  The  medical  pro- 
fession alone  is  not  able  to  cope  with  it.  The  young  men 
and  women  who  are  to  be  the  executive  health  officers  in  the 
next  generation  are  recognizing  the  need  of  special  training, 
based  on  the  principles  of  preventive  medicine,  hygiene  and 
sanitation.  Schools  of  public  health  are  coming  into  exist- 
ence and  receiving  warm-hearted  support.  The  health  ad- 
ministration of  the  future  will  be  in  the  hands  of  full-time 
officials,  who  are  adequately  paid  and  protected  in  their 
tenure  of  office,  but  who  in  return  for  these  advantages  must 
be  adequately  trained  for  their  work.  The  ability  to  use 
vital  statistics  in  public  health  work  is  an  important  part 
of  this  training.  Many  of  you  have  been  in  office  for  a  long 
time,  you  have  forgotten  most  of  your  arithmetic  —  not  to 
mention  algebra.  You  can  see  the  new  era  coming  and  you 
dread  the  new'  methods  founded  on  accurate  statistical  studies 
of  accident,  disease  and  death.  There  is  no  need  of  this  fear. 
You  can  use  statistics  as  well  as  any  one,  but  you  must  study. 
This  book  has  been  prepared  with  your  difficulties  in  mind. 

GEORGE  CHANDLER  WHIPPLE 

CAMBRIDGE,  MASS. 
January,  1919. 


CONTENTS 

CHAPTER  I 

DEMOGRAPHY 

PAGE 

Principal  divisions  of  demography  —  Demography  both  old  and 
new  —  History  of  statistics  —  Celebrated  demographers  —  Sec- 
tion of  Vital  Statistics  —  The  statistical  method  —  Need  of  the 
statistical  method  —  Why  statistics  are  thought  to  be  dry  —  Can 
you  prove  anything  by  statistics?  —  National  bookkeeping  —  Sta- 
tistics necessary  for  health  officer  —  National  vital  statistics  — 
Statistical  induction  —  Choice  of  statistical  data 1 

CHAPTER  II 
STATISTICAL  ARITHMETIC 

Statistical  processes  —  Collection  of  data  —  Statistical  units  — 
Errors  of  collection  —  Tally  sheets  —  Tabulation  —  Inexact 
numbers  —  Precision  and  accuracy  —  Combinations  of  inexact 
numbers  —  Ratios  —  Rates  —  Misuse  of  rates  —  Index  —  Com- 
putation of  rates  —  Logarithms  —  The  slide-rule  —  Classification 
and  generalization  —  Classes,  groups,  series  and  arrays  —  Gen- 
eralizations of  classes  and  groups  —  The  array  and  its  analysis  —  ' 
Groups  —  Group  designations  —  Percentage  grouping  —  Cumu- 
lative grouping  —  Averages  —  The  moving  average  —  Mechanical 
devices 17 

CHAPTER  in 
STATISTICAL  GRAPHICS 

Use  of  graphic  methods  —  Types  of  diagrams  —  The  appeal  to 
the  eye  —  Graphical  deceptions  —  Essential  features  of  a  diagram 

—  One-scale  diagrams  —  Diagrams  with  rectangular  coordinates 

—  Use  of  the  horizontal  scale  —  Plotting  figures  by  groups  — 

vii 


viii  CONTENTS 

PAGE 

Plotting  irregular  groups  —  Summation  diagrams  —  Choice  of 
scales  —  Diagrams  with  polar  coordinates  —  Double  coordinate 
paper  —  Ratio  cross-section  paper  —  Logarithmic  cross-section 
paper  —  Ruled  paper  —  Mechanics  of  diagram  making  —  Letter- 
ing —  Wall  charts  —  Use  of  color  in  diagrams  —  Component  part 
diagrams  —  Statistical  maps  —  Blue  prints  and  other  prints  — 
Reproduction  of  diagrams  —  Equation  of  curves 58 

CHAPTER  IV 
ENUMERATION  AND  REGISTRATION 

United  States  census  —  The  census  date  —  Civil  divisions  — 
Enumeration  schedule  of  1910  —  Rowley's  rules  for  enumeration 

—  Credibility  of  census  returns  —  State  censuses  —  Registration 
and  notification  —  Registration  of  births  —  Advantages  of  birth 
registration  —  Evidences  of  incomplete    registration  —  Enforce- 
ment  of  registration   law  —  Registration   of   deaths  —  Uses   of 
death    registration  —  Marriage    registration  —  Morbidity    regis- 
tration —  Notifiable    diseases  —  Incompleteness     of    morbidity 
statistics  —  Morbidity  from  non-reportable  diseases  —  Reporting 
venereal  diseases  —  Sickness  surveys  —  Other  methods  of  securing 
data  —  United  States  registration  area  for  deaths  —  United  States 
registration  area  for  births  —  Need  of  national  statistics 100 

CHAPTER  V 
POPULATION 

Estimation  of  population  —  Arithmetical  increase  —  Adjust- 
ment of  population  to  mid-year  —  Geometrical  increase  —  For- 
mula for  geometrical  increase  —  Rate  of  increase  —  Decreasing 
rate  of  growth  —  Difference  between  estimate  and  fact.  Revised 
estimates  —  Estimation  of  population  from  accessions  and  losses 

—  Estimation    of    future    population  —  Immigration  —  Graphi- 
cal method  of  estimating  population  —  Accuracy  of  state  cen- 
suses —  Urban  and  rural  population  —  Density  of  population  — 
Population  of  United  States  cities  —  Metropolitan    districts  — 
Classification  of  population  —  Color,  race,  nativity,  parentage  — 
Sex  distribution  —  Dwellings  and  families  —  Age  distribution  — 
Census  meaning  of  age  —  Errors  in  ages  of  children  —  Errors 


CONTENTS  ix 

PAGE 

due  to  use  of  round  numbers  —  Other  sources  of  error  —  Age- 
groups  —  Persons  of  unknown  age  —  Redistribution  of  population 
—  Redistribution  for  -non-censa!  years  —  Progressive  character  of 
age  distribution  —  Types  of  age  distribution  —  Standards  of  age 
distribution  —  Age  distribution  of  people  of  United  States 129 


CHAPTER  VI 
GENERAL  DEATH-RATES,  BIRTH-RATES,   MARRIAGE-RATES 

Gross,  or  general,  death-rates  —  Precision  of  death-rates  — 
Corrected  death-rates  —  Revised  death-rates  —  Variations  in 
death-rates  in  places  of  different  size  —  Errors  in  published 
death-rates  —  Rates  for  short  periods  —  Birth-rates  —  Relation 
between  birth-rates  and  death-rates  —  Fecundity  —  Marriage- 
rates  —  Divorce-rates  —  Natural  rate  of  increase  —  Comparison 
of  general  rates  —  Marriage-rates,  birth-rates  and  death-rates  in 
Sweden  —  Downward  trend  in  birth-rates  and  death-rates  — 
Variations  due  to  population  estimates  —  Birth-rates  and  death- 
rates  in  Massachusetts  —  Monthly  death-rates  in  Massachu- 
setts—  Marriage-rates  in  Massachusetts — ^Divorce-rates .  in 
Massachusetts  —  Limited  use  of  gross  death-rates  —  The  ideal 
death-rate..  186 


CHAPTER  VII 
SPECIFIC  DEATH-RATES 

Restriction  of  death-rates  —  Ages  of  Man  —  The  vision  of 
Mirza  —  Computation  of  specific  death-rates  —  Specific  death- 
rates  by  ages  and  sex  —  Specific  death-rates  as  affected  by  mari- 
tal condition  —  Specific  death-rates  and  nationality  —  Influence 
of  age  composition  of  population  on  death-rate  —  Influence  of 
racial  composition  on  death-rates  —  Chronological  changes  in 
specific  death-rates  —  Fallacy  of  concealed  classification  —  Use  of 
specific  death-rates  —  Death-rates  adjusted  to  a  standard  popu- 
lation—Examples of  adjusted  death-rates  —  Adjustment  of 
racial  differences  —  Death-rates  for  particular  diseases  —  Special 
death-rates. . .  220 


X  CONTENTS 

CHAPTER  VIII 

CAUSES  OF  DEATH' 

PAGE 

Nosography  —  Nosology  —  Purpose  of  Nosology  —  History  of 
nosography  —  International  list  [pi  causes  of  death  —  Classifi- 
cation of  diseases  in  1850  —  Present-day  classification  —  Unde- 
sirable terms  —  Synonyms  of  typhoid  fever  —  Joint  causes  of 
death  —  Classification  of  occupations  —  Nosology  not  an  exact 
science 254 


CHAPTER  IX 
ANALYSIS  OF  DEATH-RATES 

Reasons  for  analyzing  death-rates  —  Two  methods  of  analysis 
—  Useful  sub-divisions  —  Analysis  of  the  death-rate  of  a  state  — 
Comparison  of  death-rates  of  two  cities  —  Rates  not  the  only 
methods  of  comparison 299 


CHAPTER  X 
STATISTICS  OF  PARTICULAR  DISEASES 

Mortality  rate  —  Proportionate  mortality  —  Morbidity-rate  — 
Fatality  —  Inaccuracies  of  morbidity  and  fatality-rates  —  Causes 
of-  death  in  Massachusetts  —  Study  of  tuberculosis  by  age  and 
sex  in  Cambridge,  Mass.  —  Seasonal  distribution  of  deaths  from 
tuberculosis  —  Chronological  study  of  tuberculosis  —  Tuber- 
culosis and  occupation  —  Tuberculosis  and  racial  composition 
of  population  —  Diphtheria  in  Cambridge,  Mass.  —  Age  sus- 
ceptibility to  diphtheria  —  Fatality  of  diphtheria  —  Chrono- 
logical study  of  diphtheria  —  Urban  and  rural  distribution  of 
diphtheria  —  Statistical  study  of  typhoid  fever  —  Age  distribu- 
tion of  typhoid  fever  —  Seasonal  distribution  of  typhoid  fever  — 
Chronological  reduction  in  typhoid  fever  —  Statistics  of  cancer  — 
Further  studies  of  particular  diseases 308 


CONTENTS  xi 

CHAPTER  XI 

STUDIES   OF  DEATHS  BY  AGE  PERIODS 

PAGE 

Infant  mortality  —  Some  definitions  —  Pre-natal  deaths  — 
Infant  mortality  and  specific  death-rates  of  infants  —  First- 
year  death-rate  —  Methods  of  stating  infant  mortality  —  Chron- 
ological reduction  in  infant  mortality  —  Reasons  for  the  de- 
creasing infant  mortality  —  Infant  mortality  in  different  places 

—  Deaths  of  infants  at  different  ages  —  Specific  death-rates  of 
infants  at  different  .ages  —  Expectation  of  lif e  at  different  ages  — 
Infant  mortality  by  age  periods  —  Causes  of  infant  deaths  —  The 
Johnstown  studies  —  Other  studies  of  the  Childrens'  Bureau  — 
Infant   mortality  problems  —  Maternal  mortality  —  Childhood 
mortality  —  Diseases  of  early  childhood  —  Proportionate  mortal- 
ities during  school  age  —  Proportionate  mortalities  at  higher  ages 

—  Median  age  of  persons  living  —  Average  age  at  death 339 

CHAPTER  XII 
PROBABILITY 

Natural  frequency  —  Coin  tossing  —  Chance  —  Binomial  the- 
orem —  Chance  and  natural  phenomena  —  Frequency  curves, 
including  skew  curves  —  Frequency  curves  shown  by  summation 
diagrams  —  Deviation  from  the  mean  —  Standard  deviation  — 
Coefficient  of  variation  —  Computation  of  coefficient  from  grouped 
data  —  Probable  error  —  Doubtful  observations  —  The  proba- 
bility scale  —  Probability  cross-section  paper  —  Another  use  of 
probability  —  The  frequency  curve  as  a  conception 376 

CHAPTER  XIII 
CORRELATION 

Correlation  —  Causal  relations  —  Correlation  and  causality  — 
Laws  of  causation  —  Methods  of  correlation  —  Galton's  coefficient 
of  correlation  —  Example  of  low  correlation  —  Correlation  shown 
graphically  —  Correlation  table  —  Use  of  mathematical  formulae 

—  Secondary  correlation  —  The  lag  —  Coefficient  of  correlation 
and  the  lag  —  Other  secondary  correlations  —  The  epidemiologist's 

use  of  correlation 402 


xii  CONTENTS 

CHAPTER   XIV 

LIFE  TABLES 

PAGE 

Life  tables  —  Probability  of  living  a  year  —  Mortality  tables  — 
Most  probable  lifetime  —  "Vie  probable"  —  Expectation  of 
life  —  Comparison  of  the  three  methods  —  Life  tables  based  on 
living  populations  —  Mathematical  formulae  —  Early  history  of 
life  tables  —  Recent  life  tables  —  United  States  Life  Tables:  1910 
—  A  few  comparisons 422 

CHAPTER  XV 
A  COMMENCEMENT  CHAPTER 

The  day  after  commencement  —  Military  statistics  —  Army 
diseases  —  Effect  of  the  war  on  demography  —  Hospital  statisr 
tics  —  Statistics  of  industrial  disease  —  List  of  occupations  — 
Economic  conditions  and  health  —  Accidents  —  Age  distribution 
of  poliomyelitis  —  'Averages  and  median  age  of  persons  living  — 
Average  age  at  death  —  The  Mills-Reincke  phenomenon  —  The 
sanitary  index  —  Publication  of  reports 436 

APPENDIX  I 
REFERENCES 

General  text-books  —  Periodicals  —  Reports  —  Demography  — 
Arithmetic  —  Graphics  —  Census  —  Population  —  Death-rates  — 
Probability  —  Correlation  —  Life  tables 459 

APPENDIX  II 

THE  MODEL  STATE  LAW  FOR  MORBIDITY  REPORTS 465 

APPENDIX  III 

THE  MODEL  STATE  LAW  FOR  THE  REGISTRATION  OF  BIRTHS  AND 
DEATHS 472 

APPENDIX  IV 

TABLE  OF  LOGARITHMS  OF  NUMBERS..  .  491 


VITAL  STATISTICS 


CHAPTER  I 
DEMOGRAPHY 

Broadly  speaking  demography  is  the  statistical  study 
of  human  life.  It  deals  primarily  with  such  vital  facts 
as  birth,  physical  growth,  marriage,  sickness  and  death 
and  incidentally  with  political,  social,  educational,  religious, 
sanitary,  hygienic  and  medical  matters.  In  a  somewhat 
narrower  sense  demography  is  used  as  a  synonym  for  vital 
statistics. 

The  word  "demography"  is  derived  from  the  Greek 
words  demos,  people,  and  grapho,  to  write.  It  is  in  com- 
mon use  in  Europe,  but  is  not  as  well  known  or  its  meaning 
as  well  understood  in  America.  High  authority  for  its 
use  is  found  in  the  name  of  that  most  important  triennial 
gathering  of  physicians  and  sanitarians,  the  International 
Congress  of  Hygiene  and  Demography. 

Demography  cannot  be  called  a  science  in  the  sense  that 
it  is  a  classified  body  of  knowledge  from  which  laws  have 
been  developed  and  established.  But  all  sciences  in  their 
evolution  go  through  a  descriptive  stage  in  which  data  are 
collected  and  hypotheses  tested.  So  regarded  demog- 
raphy may  be  called  a  science,  —  the  science  of  human 
generation,  growth,  decay  and  death  as  studied  by  statis- 
tical methods. 

1 


2  DEMOGRAPHY 

The  principal  divisions  of  demography.  —  Demography 
may  be  said  to  include  the  following  major  subjects: 

1.  Genealogy,  which  considers  individual  ancestries  and 

personal  records. 

2.  Human  eugenics,   which   considers  heredity  from  a 

scientific  standpoint,  and  is  to  a  large  extent  the 
application  of  the  statistical  method  to  genealogy. 

3.  The  census,  that  is,  the  collection  of  social,  political, 

religious  and  educational  facts  concerning  popula- 
tion, usually  by  the  method  of  governmental  enum- 
eration. 

4.  Registration  of  vital  facts,  such  as  those  concerning 

birth,  marriage,  divorce,  sickness  and  death,  usu- 
ally under  governmental  direction  and  by  the  use 
of  individual  records. 

5.  Vital  statistics,  which  is  the  application  of  the  statis- 

tical method  to  the  study  of  these  vital  facts. 

6.  Biometrics,  which  includes  anthropometric  studies  of 

human  growth,  stature,  strength,  etc. 

7.  Pathometrics,  that  is,  statistical  pathology,  which  in- 

cludes detailed  studies  of  diseases  and  their  rela- 
tions to  the  human  body.     These  facts  are  obtained 
largely  in  hospitals,  by  health  department  labora- 
tories and  by  life  insurance  companies. 
Demography  both  old  and  new. — 'The  word  "demog- 
raphy "  has  come  into  use  during  the  last  generation,  and 
has  not  even  now  taken  its  proper  place  in  the  list  of  recog- 
nized sciences;  but  the  gathering  together  of  facts  relating  to 
human  life  and  the  expression  of  these  facts  numerically 
has  been  practiced  from  time  immemorial. 

Some  parts  of  demography  are  older  than  others.  Gene- 
alogy is  very  old.  "Adam  lived  an  hundred  and  thirty 
years,  and  begat  a  son  in  his  own  likeness,  after  his  image; 
and  called  his  name  Seth:  And  Seth  lived  an  hundred  and 


HISTORY  OF  STATISTICS  3 

five  years  and  begat  Enos:  And  Enos  lived  ninety  years 
and  begat  Cainau;  And  Cainau  lived  seventy  years  and 
begat  Mahalaleel:  "  And  so  it  goes  on.  Hundreds  of 
years  before  Christ  enumerations  of  the  people  were  made 
for  purposes  of  taxation  and  for  other  reasons,  as  one  may 
read  in  the  histories  of  Egypt,  Persia,  Judaea,  Greece, 
Rome  or  China. 

Many  fragmentary  data  relating  to  births,  deaths  and 
marriages  were  recorded  in  the  old  church  registers  of 
England.  Capt.  John  Graunt  compiled  the  vital  statis- 
tics for  the  city  of  London  in  1662,  which  attracted  much 
attention  at  the  time.  In  referring  to  the  Great  Plague 
in  London  in  1666  Pepys  tells  about  the  published  "  bills," 
that  is,  the  list  of  the  dead,  and  gives  their  statistics. 

But  the  application  of  statistics  and  the  scientific  method 
to  genealogy  is  relatively  modern  and  so  are  the  develop- 
ments of  biometry  and  pathometry.  Sir  Francis  Galton 
and  Professor  Karl  Pearson,  of  England,  have  been  leaders 
in  this  and  may  almost  be  said  to  have  founded  a  new 
school  of  statisticians. 

Demography,  therefore,  is  both  an  old  and  a  new 
science. 

History  of  statistics.  —  The  word  "  statistics  "  is  nearly 
two  centuries  old,  being  first  used  by  Gottfried  Achenwall, 
who  lived  in  Jena,  1719-1772.  Before  that  we  learn  of  the 
political  arithmeticians  in  France  and  Italy  and  of  Aristotle 
who  used  statistics  in  describing  and  comparing  different 
states.  The  systematic  publication  of  the  details  of  official 
statistics  owes  its  origin  to  Anton  Biischvig,  1724-1793,  who 
published  a  voluminous  work  on  historiography  and  founded 
a  magazine  in  which  statistics  for  various  countries  were 
brought  together  and  compared.  Crome  in  1785  published 
important  Tabellen-Statistik  which  contained  various  data 
in  regard  to  population  in  Germany. 


4  DEMOGRAPHY 

Many  well-known  scientists  undertook  statistical  in- 
vestigations. Edmund  Halley,  1656-1742,  the  astronomer 
who  discovered  the  comet  which  bears  his  name,  compiled 
in  1693  a  series  of  mortality  tables  and  calculated  the  ex- 
pectation of  life  at  each  age  and  thus  laid  the  foundation 
for  scientific  life  insurance.  In  1713  Bernouilli,  noted  for 
his  hydraulic  studies,  demonstrated  a  theory  of  proba- 
bilities which  a  century  later,  1813,  was  perfected  by 
Laplace  in  his  masterly  treatise  "Theorie  analytique  des 
probabilites." 

John  Graunt,  already  mentioned,  laid  the  foundations 
for  vital  statistics  when  in  1662  he  wrote  his  remarkable 
"Natural  and  Political  Observations  upon  the  Bills  of 
Mortality." 

In  1741  Job.  Peter  Sussmilch  (1707-1767)  published  an 
important  work  on  vital  statistics  from  which  he  attempted 
to  draw  some  far-reaching  moral  deductions.  He  tried  to 
demonstrate  statistically  the  doctrine  of  the  "  Natural 
Order."  From  the  equality  of  the  sexes  at  marriage  (at 
birth  his  ratio  is  21  sons  to  20  daughters)  he  derives  the 
command  of  monogamy.  From  a  comparison  of  urban 
and  rural  death-rates  (in  cities  one  death  to  25  to  32  per- 
sons, and  in  the  country,  one  to  every  40  to  45  persons) 
he  censures  the  unnaturalness,  immorality,  and  luxury  of 
city  life,  " proving  statistically"  that  these  bring  down 
the  wrath  of  God. 

With  the  accumulation  of  statistical  data  various  di- 
vergencies began  to  appear.  The  political  economists, 
headed  by  Adam  Smith  ("  Wealth  of  Nations,"  1776)  and 
followed  by  Malthus  (1804)  and  others,  separated  them- 
selves from  the  realm  of  general  statistics.  Hitter  (1779- 
1859)  led  the  study  of  geography  apart.  At  the  end  of 
the  18th  century  the  life  insurance  companies  also  drew 
away  from  the  considerations  of  general  populations,  and, 


.  THE  WORLD'S  GREAT  DEMOGRAPHERS      5 

by  reason  of  the  accumulation  of  their  own  data  relating 
to  deaths,  began  to  depend  upon  them  alone.  This  split- 
ting up  of  the  general  science  of  statistics  and  the  multi- 
plication of  the  practical  applications  of  statistics  led  to  an 
increasing  laxity  in  method,  a  condition  which  we  have 
hardly  yet  outgrown. 

Quetelet,  1796-1874,  aroused  much  enthusiasm  over 
statistics  as  "the  queen  of  all  the  sciences."  His  work  on 
probability  was  justly  famous  and  was  an  inspiration  to 
Florence  Nightingale.  Since  his  time,  however,  this  branch 
of  the  subject  has  been  more  commonly  considered  as  a 
part  of  pure  mathematics  and  is  treated  in  books  on 
"Least  Squares,"  the  law  of  error,  and  precision  of  meas- 
urements. 

Finally,  we  come  to  the  brilliant  works  of  Galton,  Karl 
Pearson  and  others,  already  mentioned. 

The  history  of  statistics  is  a  fascinating  one,  as  it  flits 
around  from  country  to  country,  now  flourishing  in  Italy, 
then  in  France,  England,  Denmark,  Germany,  England 
again.  The  United  States  has  had  many  able  statisticians 
but  few  statistical  mathematicians  worthy  to  be  compared 
to  Laplace,  Quetelet  or  Karl  Pearson. 

The  world's  great  demographers.  —  Some  of  the  great- 
est scientists  of  the  world  have  been  enthusiastic  statisti- 
cians. In  some  cases  their  greatness  has  been  due  to  their 
statistical  skill.  Even  at  the  present  time  it  is  safe  to  say 
that  the  most  successful  health  officers  are  good  statisti- 
cians, although  it  does  not  follow  that  all  good  statisticians 
are  successful  health  officers. 

The  following  is  a  short  list  of  men,  not  now  living,  who 
have  made  important  contributions  to  the  study  of  statis- 
tics, —  especially  vital  statistics.  The  student  will  find  it 
interesting  to  add  to  this  list. 


6  DEMOGRAPHY 

Capt.  John  Graunt  (1620-1674),  of  England. 
Melchiorre  Gioja  (1767-1829),  of  Italy. 
Sir  Francis  Gallon  (1822-1911),  of  England. 
William  Farr  (1807-1883),  of  England. 
Louis  A.  Bertillon  (1821-1883),  of  France. 
Alphonse  Bertillon  (1853-1914),  of  France. 
Edwin  Chadwick  (1800-1890),  of  England. 
Florence  Nightingale  (1820-1910),  of  England. 
Edward  Jarvis  (1803-1884),  of  Boston,  Mass. 
Lemuel  Shattuck  (1793-1859),  of  Boston. 
Samuel  Warren  Abbott  (1827-1894),  of  Boston. 
Carroll  D.  Wright  (1840-1909),  of  Massachusetts. 

Section  of  Vital  Statistics.  —  The  American  Public  Health 
Association  has  always  manifested  a  keen  interest  in  vital 
statistics.  Some  of  the  reports  of  its  committees  have  had 
a  far-reaching  effect.  In  1907  a  Section  of  Vital  Statistics 
was  organized  in  this  association,  and  since  that  date  the 
journal  of  the  association,  now  known  as  the  American  Jour- 
nal of  Public  Health,  has  contained  many  important  articles 
on  the  subject.  Membership  in  this  section  is  open  to  regis- 
tration officials,  statisticians,  epidemiologists,  sanitarians 
and  other  members  of  the  American  Public  Health  Associa- 
tion who  are  interested  in  vital  statistics. 

The  "  Statistical  Method."  —  Statistics  are  facts  ex- 
pressed by  figures.  Strictly  speaking  a  birth  reported  and 
recorded  officially  is  not  a  statistic,  but  a  vital  fact;  yet 
inasmuch  as  reported  and  recorded  births  are  commonly 
counted  and  the  results  expressed  numerically  it  is  appro- 
priate to  regard  such  a  birth  record  as  a  statistical  unit 
or  item,  that  is,  as  a  statistic.  It  is  not  customary,  how- 
ever, to  use  the  word  in  the  singular  number. 

By  expressing  facts  by  figures  it  is  possible  to  arrange 
them  in  various  ways  for  study  and  comparison,  as,  for 
example,  in  tables  and  graphs;  to  classify  them;  to  make 
generalizations;  to  use  them  in  logical  processes  and  thus 


WHY  WE  NEED  TO  USE  THE  STATISTICAL  METHOD     7 

to  draw  inferences  and  conclusions  based  on  the  facts. 
The  various  mathematical  processes  used  for  this  purpose 
are  collectively  known  as  the  statistical  method. 

Some  of  these  processes  are  quite  elaborate  and  involve 
complicated  mathematical  methods  and  conceptions,  such 
as  the  laws  of  variation,  dispersion,  correlation  and  prob- 
ability. For  many  years  there  has  been  a  discussion  as 
to  whether  " statistics"  should  be  regarded  as  a  distinct 
science,  ranking  with  physics,  chemistry  and  biology  or 
merely  as  a  method.  Westergaard  expresses  the  truest 
conception  when  he  says  that  "it  is  an  auxiliary  science  in 
many  branches  of  human  thought."  "There  are  some 
statisticians  who  are  statisticians  and  there  are  some  stat- 
isticians who  are  mathematicians."  There  are  theories 
of  statistics  which  comprise  a  very  considerable  part  of 
mathematics.  Volumes  have  been  written  on  the  Calcu- 
lus of  Probabilities,  on  Least  Squares,  on  Variation.  On 
the  other  hand,  many  of  the  statistical  processes  are  ex- 
tremely simple  and  do  not  get  beyond  the  bounds  of 
ordinary  arithmetic.  The  simple  processes  have  a  wide 
general  use;  the  more  elaborate  processes  have  their  place 
but -are  not  commonly  applicable  or  necessary. 

Why  we  need  to  use  the  statistical  method.  —  People 
who  do  not  like  mathematics  often  say  "Oh!  Pshaw! 
Why  do  we  have  to  study  statistics?  Of  what  good  are 
they?  "  The  answer  is  that  in  a  big  world  we  have  to 
deal  with  many  facts  and  the  statistical  method  enables 
us  to  abbreviate  facts,  to  concentrate  them  so  that  we 
can  more  readily  study  and  compare  them  and  find  out 
what  they  mean.  If  you  want  to  live  in  a  little  world  and 
deal  with  only  a  few  facts  then  you  do  not  need  statistics. 
The  head  of  a  small  factory  may  remember  the  wages  of 
each  one  of  his  employees.  Tom  gets  ten  dollars  a  week, 
Fred  gets  twelve,  Sam  and  Bill  each  get  fifteen  and  Henry 


8  DEMOGRAPHY 

gets  sixteen  dollars.  But  the  head  of  a  large  factory 
where  there  are  a  hundred  hands  cannot  carry  all  these 
facts  in  mind.  The  bookkeeper  of  course  has  a  record  of 
them,  very  necessary  for  pay-day.  The  head  of  the  fac- 
tory may  know,  however,  that  ten  of  the  employees  get 
sixteen  dollars  a  week,  fifteen  get  twelve  dollars  and  sev- 
enty-five get  ten  dollars.  The  factory  superintendent 
needs  these  statistics.  He  lives  in  a  large  world.  The 
village  gossip  knows  the  dates  of  all  the  births,  marriages 
and  deaths  in  town  since  January  first,  but  she  lives  in  a 
little  world.  To  ^compare  these  facts  with  similar  facts 
for  the  next  town  and  the  one  next  to  tnat  requires  that 
the  facts  be  expressed  in  figures.  Statistics  enable  one  to 
enlarge  his  horizon. 

Why  are  statistics  thought  to  be  "  dry"  ?  —  Statistics 
have  the  popular  reputation  of  being  dry,  uninteresting, 
or,  as  Shakespeare  would  say,  —  "flat,  stale  and  unprofit- 
able." This  is  very  natural,  for  all  figures  look  alike.  If 
we  are  considering  one  hundred  and  thirty-seven  tons  of 
coal  we  use  the  figures  137  and  if  we  are  talking  about  the 
same  number  of  American  Beauty  roses  we  also  use  the 
figures  137.  If  we  think  only  of  the  figures  we  see  no 
difference  between  these  statistics.  It  does  not  take 
much  imagination  to  visualize  137  roses,  their  beauty  and 
their  odor;  it  takes  more,  perhaps,  to  visualize  137  tons  of 
coal.  And  if  37  of  the  roses  are  said  to  be  yellow,  60 
white  and  40  red,  we  can  visualize  the  whole  mass  even 
if  we  know  that  they  are  mixed.  The  reason  why  statis- 
tics are  "dry  "  is  because  people  do  not  try  to  visualize 
them.  If  you  don't  try  to  visualize  the  statistics  the 
figures  are  commonplace  and  of  course  uninteresting,  while 
if  you  do  try  the  mental  effort  is  tiring.  Moreover,  there 
is  a  real  difficulty  and  that  is  our  inability  to  visualize 
very  large  figures.  I  may  be  able  to  visualize  a  hundred 


CAN  ONE  PROVE  ANYTHING  BY  STATISTICS         9 

dollars,  but  I  confess  not  to  be  able  to  visualize  a  million 
dollars,  even  though  I  know  that  it  is  one  thousand  times 
as  much  as  one  thousand  dollars.  Also  visualization  is 
lost,  or  at  any  rate  confused,  when  we  begin  to  perform 
mathematical  operations  with  our  statistics. 

The  way  to  prevent  statistics  from  being  "dry"  is  to 
keep  in  mind  that  statistics  are  not  merely  figures,  but  are 
figures  which  stand  for  facts. 

Is  it  true  that  "  you  can  prove  anything  by  statistics  "  ? 
-  We  often  hear  it  said  "Oh!  you  can  prove  anything  by 
statistics."  Is  this  true  ?  Suppose  we  substitute  the  mean- 
ing of  statistics  and  say  "you  can  prove  anything  by 
facts  if  expressed  in  figures."  Obviously  this  is  not  so. 
Facts  are  facts  whether  expressed  in  figures  or  not.  If 
the  conclusions  are  wrong  the  trouble  lies  not  in  the  sta- 
tistics but  in  the  way  they  are  used.  The  drawing  of  con- 
clusions is  the  function  of  logic,  a  process  of  reasoning, 
and  fallacious  reasoning  should  not  be  charged  against 
statistics. 

And  yet  there  is  something  which  underlies  the  popular 
statement.  When  figures  are  used  to  express  facts,  and 
when  the  logical  processes  are  applied  to  figures,  divorced 
in  the  mind  from  the  facts  for  which  they  stand,  it  is  easy 
for  fallacies,  to  creep  in  without  being  recognized;  it  is 
easy  to  compare  things  which  ought  not  to  be  compared, 
to  generalize  from  inadequate  data,  and  to  commit  all  sorts 
of  illogical  errors.  Thus  the  unscrupulous  may  fool  the 
unwary,  and  the  innocent  may  fool  themselves.  Hence 
to  use  statistics  properly  one  must  be  able  not  only  to 
visualize  the  facts  but  to  think  logically.  Students  who 
would  be  statisticians  should  therefore  study  formal  logic. 
Some  of  the  common  fallacies  in  the  use  of  statistics  will 
be  considered  on  later  pages.  Honesty  and  conservatism 
are  essential  qualities  for  the  makers  and  users  of  statistics. 


10  DEMOGRAPHY 

There  are  numerous  works  on  logic.  One  of  the  best  is 
"The  Principles  of  Science,"  by  W.  Stanley  Jevons.  It 
treats  not  only  of  logic  but  of  the  scientific  method  in 
general. 

The  national  value  of  "  Vital  Bookkeeping."  —  It  is  of 
the  greatest  importance  to  a  nation  that  accurate  records 
be  kept  of  its  vital  capital,  of  its  gains  by  birth  and  immi- 
gration and  of  its  losses  by  death  and  emigration,  for  a 
nation's  true  wealth  lies  not  in  its  lands  and  waters,  not  in 
its  forests  and  mines,  not  in  its  flocks  and  herds,  not  in  its 
dollars,  but  in  its  healthy  and  happy  men,  women  and 
children.  A  well  man  is  worth  more  to  a  nation  than  a 
sick  man;  a  man  in  the  prime  of  life  is  of  more  immediate 
worth  than  an  old  man  or  a  child,  a  married  man  is  poten- 
tially a  greater  asset  than  a  single  man.  Hence,  in  a  na- 
tion's vital  bookkeeping  the  number  of  people,  their  age 
and  sex  and  conjugal  condition,  their  parentage,  their 
health,  the  rate  of  births  and  deaths,  are  matters  of  great 
moment.  Their  environment  is  also  important;  their  con- 
centration in  cities  and  villages  and  congested  areas,  their 
mode  of  housing,  their  occupation,  their  state  of  intelli- 
gence, their  economic  condition,  their  knowledge  of  sani- 
tation, all  contribute  to  the  sum  total  of  their  usefulness 
to  themselves  and  to  society. 

Vital  bookkeeping  is  carried  on  much  as  ordinary  book- 
keeping; there  are  daily  entries  of  accessions  and  losses  as 
they  occur,  corresponding  to  receipts  and  payments;  there 
are  weekly  statements,  monthly  statements  and  annual 
statements;  and  at  longer  intervals  there  is  a  taking 
account  of  stock,  that  is,  a  census.  One  important  differ- 
ence, however,  should  be  noted.  Accounts  are  accurate 
records  of  transactions  and  if  properly  kept  an  exact  bal- 
ance will  be  obtained  Vital  statistics  are  not  always 
accurate,  the  individual  data  are  incomplete  and  subject 


STATISTICS  NECESSARY  FOR  HEALTH  OFFICER      11 

to  error;  the  results,  therefore,  lack  the  precision  of  mone- 
tary accounts.  It  is  necessary  to  keep  this  fact  constantly 
in  mind  when  interpreting  the  results  of  statistical  studies. 
An  understanding  of  the  principles  of  the  arithmetic  of 
inexact  numbers  and  of  the  theory  of  probability  is  essen- 
tial. 

Vital  statistics  are  useful  for  many  purposes.  To  the 
historian  they  show  the  nation's  growth  and  mark  the 
flood  and  ebb  of  physical  life;  to  the  economist  they  in- 
dicate the  number  and  distribution  of  the  producers  and 
consumers  of  wealth;  to  the  sanitarian  they  measure  the 
people's  health  and  reflect  the  hygienic  conditions  of  the 
environment;  to  the  sociologist  they  show  many  things 
relating  to  human  beings  in  their  relations  one  with  another. 

Vital  statistics  necessary  for  health  officer.  —  Vital  sta- 
tistics are  not  to  be  collected  and  used  as  mere  records  of 
past  events:  an  even  more  important  use  is  that  of  prophe- 
sying the  future.  An  engineer  in  planning  a  water  supply 
to  last  for  a  generation  estimates  the  future  population  by 
the  previous  rate  of  growth;  so  also  in  laying  out  a  system 
of  streets  and  sewers  and  transportation  service.  The 
whole  idea  of  city  planning  is  fundamentally  based  on  the 
use  of  the  vital  statistics  of  what  has  been  as  a  means  of 
estimating  what  is  to  be. 

The  health  officer  of  a  city  or  he  whose  duty  it  is  to  col- 
lect and  record  the  vital  statistics  should  study  them  as 
soon  as  received  and  not  wait  until  some  convenient  day 
when  other  work  is  slack  and  then  merely  tabulate  and 
make  averages  for  formal  reports  and  permanent  records. 
Vital  statistics,  especially  those  of  morbidity,  should  be 
studied  in  the  making,  and  just  as  the  meteorologist  reads 
his  instruments  daily  in  order  to  forecast  the  weather  and 
give  warnings  of  the  coming  hurricane,  so  the  efficient 
health  officer  will  daily  study  the  reports  of  new  cases  of 


12  DEMOGRAPHY 

disease  in  order  that  he  may  be  forewarned  of  an  impend- 
ing epidemic  and  take  measures  to  check  its  ravages. 

No  lighthouse  keeper  on  a  rocky  coast  is  charged  with 
greater  responsibility  than  he  who  is  set  to  watch  the 
signs  of  coming  pestilence  from  the  conning  tower  of  the 
health  department.  Making  another  comparison,  we  may 
say  that  the  health  service  should  be  organized  for  rapid 
work  like  a  fire  department,  with  its  rapid  facility  for 
learning  that  a  fire  exists  and  its  ever  ready  apparatus  for 
extinguishing  the  blaze.  If  the  fire  alarm  is  not  rung, 
the  blaze  will  spread,  and  if  cases  of  disease  are  not  reported 
the  epidemic  will  likewise  spread.  The  duty  of  reporting 
cases  of  infectious  disease  rests  upon  the  practicing  physi- 
cians, and  thereby  hangs  a  sad  and  discouraging  tale. 

National  vital  statistics.  —  It  has  now  become  well  rec- 
ognized that  the  maintenance  of  accurate  records  of  vital 
statistics  is  a  proper  governmental  function,  and  no  nation, 
state  or  city  can  be  considered  as  having  a  complete  gov- 
ernmental equipment  which  does  not  provide  for  the 
proper  collection  and  permanent  record  of  such  statistics. 
But,  as  will  be  seen,  even  our  longest  governmental  rec- 
ords are  relatively  short,  and  for  that  reason  we  should 
be  careful  in  drawing  general  conclusions  from  them. 

Sweden.  —  Of  modern  nations  Sweden  has  a  just  claim 
to  the  longest  unbroken  series  of  vital  statistics.  In  1741 
registration  of  births,  marriages  and  deaths  was  begun  in 
all  parishes  and  since  1749  a  census  has  been  taken  each 
year.  The  principal  data  for  this  long  period  (1750-1900), 
were  given  in  a  most  valuable  paper  by  Sundbarg  at  the 
International  Congress  of  Hygiene  and  Demography  in 
Berlin  in  1907. 

France.  —  In  1790  Lavoisier  (1743-1794),  after  the 
French  Revolution,  collected  extensive  data  relating  to 
the  population  of  that  country,  the  amount  of  land  under 


NATIONAL  VITAL  STATISTICS  13 

cultivation,  etc.,  but  the  first  actual  enumeration  of  the 
inhabitants  of  Paris  was  not  made  until  1817. 

England.  —  In  England  the  old  parish  records  date  back 
at  least  to  1538,  when  Henry  VIII  ordered  all  parsons, 
vicars  and  curates  to  keep  true  and  exact  records  of  all 
weddings,  christenings  and  burials.  It  was  not  until  1801 
that  a  national  census  was  taken,  and  it  was  not  until  1851 
that  a  complete  census  was  made. 

United  States  of  America.  —  America  is  far  behind  other 
civilized  countries  in  its  records  of  vital  statistics.  There 
is  no  national  registration  system,  no  complete  national 
record  of  births  and  deaths.  This  results  from  our  dis- 
tributive form  of  government,  the  control  of  such  matters 
being  a  state  or  municipal  function,  not  a  federal  one. 
The  records  vary  greatly  in  different  parts  of  the  country. 
Some  of  the  older  states  like  Massachusetts  and  New 
Jersey  possess  fairly  accurate  records  that  extend  back  for 
several  decades,  but  in  some  of  the  western  and  southern 
states  the  records  are  either  absent  or  so  incomplete  as  to 
be  worthless.  At  the  time  of  the  last  census,  in  1910,  the 
registration  area  where  the  death  records  were  considered 
accurate  enough  to  warrant  their  being  published  included 
only  58  per  cent  of  the  total  population  of  the  country. 
This  condition  of  affairs  may  be  charitably  regarded  as  a 
youthful  sin  of  omission,  but  if  it  is  much  longer  contin- 
ued it  will  be  nothing  less  than  a  national  disgrace.  The 
health  statistics  of  our  best  administered  cities  are  much 
inferior  to  the  published  vital  statistics  of  European  cities, 
as,  for  example,  those  of  Hamburg,  Germany.  The  United 
States  Census  Bureau,  now  permanent,  has  become  in- 
creasingly efficient  in  recent  years,  and  its  reports  are  of 
much  value,  but  not  until  a  centralized  public  health  serv- 
ice has  been  secured  will  the  nation's  vital  statistics  be  put 
upon  a  high  plane  of  comprehensiveness  and  accuracy. 


14  DEMOGRAPHY 

The  importance  of  statistical  induction.  —  In  using  sta- 
tistics we  necessarily  employ  the  methods  of  logical  think- 
ing comprised  in  what  is  termed  "  induction,"  methods  by 
which  general  tendencies  and  laws  are  drawn  out  of  accu- 
mulations of  facts. 

Statistical  induction  may  be  said  to  be  one  of  the  most 
potent  weapons  of  modern  science.  Referring  to  it  Royce 
says  that  the  technique  of  statistical  induction  consists 
wholly  in  learning  how  to  take  fair  samples  of  the  facts  in 
question,  and  how  to  observe  these  facts  accurately  and 
adequately. 

Statistics  are  being  constantly  invoked  for  testing  hy- 
potheses in  all  branches  of  science.  This  involves  four 
distinct  processes,  — first,  the  choice  of  a  good  hypothesis; 
second,  the  computation  of  certain  consequences,  all  of 
which  must  be  true  if  the  hypothesis  is  true;  third,  the 
choice  of  a  fair  sample  of  these  consequences  for  a  test; 
fourth,  the  actual  test  of  each  of  these  chosen  hy- 
potheses. 

Deductive  reasoning  as  well  as  inductive  reasoning  is 
involved -in  the  use  of  vital  statistics.  It  is  perhaps  the 
natural  order  of  mental  processes  for  the  mind  pursuing 
an  inductive  study  to  leap  ahead  to  some  conclusion  and 
then  fill  in  the  intervening  steps  by  working  backward  by 
deduction. 

It  is  by  the  application  of  the  principles  of  logic  that 
the  statistician  is  able  to  keep  his  conclusion  within  rea- 
sonable bounds. 

Choice  of  statistical  data.  —  First,  there  is  the  complete 
statistical  study  which  includes  a  full  count  of  all  the  units 
within  the  desired  area  or  within  the  specified  time.  This 
method,  of  course,  brings  the  surest  results,  but  it  is  often 
impossible.  Second,  is  the  monographic  method,  a  pro- 
cedure in  which  a  detailed  and  exact  study  is  made  of  a 


EXERCISES  AND  QUESTIONS  15 

particular  group.  Where  the  group  selected  for  study  is 
a  well-chosen  type  the  application  of  this  method  yields 
valuable  results  but  there  is  danger  in  generalizing  from 
monographic  researches.  The  third  method  is  the  repre- 
sentative method,  a  study  of  certain  selected  parts  repre- 
sentative of  the  whole.  This  is  analogous  to  the  method 
of  the  analytical  chemist  where  chosen  samples  are  analyzed 
and  the  results  applied  to  the  whole.  The  value  of  this 
method  depends  upon  the  accuracy  of  the  sampling  process 
quite  as  much  as  upon  the  enumeration  of  the  facts  em- 
braced by  the  sample.  The  representative  method  is 
widely  used.  There  are  two  general  methods  of  sampling. 
One  is  that  of  random  selection,  the  other  is  that  of  mix- 
ture and  subdivision.  The  object  in  both  cases  is  the  same, 
—  to  secure  a  sample  truly  representative  of  the  whole. 
The  tendency  to  take  samples  of  the  obvious  and  the 
accessible  is  one  that  must  be  constantly  struggled  against. 


EXERCISES  AND    QUESTIONS 

1.  How  can  vital  statistics  be  used  to  determine  relative  values  in 
public  health  activities?     [See  Am.  J.  P.  H.,  Sept.,  1916,  p.  916.] 

2.  Describe  the  common   method  used  in   compiling  genealogies. 
[Consult    some    systematic    genealogy,  —  say    that    of    your    own 
family.] 

3.  Prepare  a  diagram  of  your  own  ancestry,  giving  the  names  of 
your  father  and  mother,  the  dates  of  their  birth  (and  death)  and  their 
birthplaces;    also  the  same  information  as  to  your  two  grandfathers 
and  your  two  grandmothers;  your  four  great-grandfathers,  etc.,  as  far 
as  the  information  can  be  readily  obtained. 

4.  Who  was  Mendel  and  what  is  the  Mendelian  law?     [See  Rose- 
nau's  Preventive  Medicine  and  Hygiene,  Chapter  on  Heredity  and 
Eugenics.] 

5.  What  are  the  primary  laws  of  heredity  and  eugenics? 

6.  What  information  can  you  give  as  to  the  heights  of  your  father  and 
mother,  your  grandfathers  and  grandmothers?     Can  you  illustrate  any 


16  DEMOGRAPHY 

of  the  laws  of  heredity,  as  to  height,  color  of  hair  or  any  other  char- 
acteristics, from  your  own  family  records? 

7.  Can  you  suggest  a  schedule  of  anthropometric  data  to  be  kept  for 
each  person  as  a  matter  of  family  record? 

8.  Write  a  short  biographical  sketch  of  some  person  famous  for  work 
in  statistics,  demography  or  vital  statistics.      (Name  to  be  assigned 
by  the  instructor.) 


CHAPTER  II 
STATISTICAL  ARITHMETIC 

Statistical  processes.  —  The  principal  processes  used  in 
the  study  of  vital  statistics  are  these : 
Collection  of  the  facts. 
Classification  of  the  facts. 
Generalization  from  the  facts. 
Comparison  of  the  facts. 

Drawing  conclusions  from  the  study  of  the  facts. 
Display  of  the  facts. 

Collection  of  data.  —  There  are  two  primary  methods  of 
obtaining  the  data  needed  in  demography  —  enumeration 
and  registration.  In  the  first  case  the  statistician  goes  or 
sends  to  get  the  facts.  The  persons  employed  are  enumer- 
ators or  inspectors.  This  is  the  method  of  census  taking 
and  is  described  in  another  chapter.  In  the  second  case 
the  facts  are  reported  to  the  statistician  in  accordance  with 
established  rules  and  regulations.  For  example,  physicians 
and  undertakers  are  required  to  send  notices  of  deaths  and 
burials  to  the  proper  authorities.  Some  of  the  methods 
in  common  use  and  the  laws  which  govern  the  reporting  of 
vital  facts  are  described  later  on. 

It  is  of  vital  importance  to  make  sure  that  the  data 
collected  are  sufficient  in  kind  and  number  for  the  purpose 
for  which  the  statistics  are  intended.  It  saves  time  and 
labor  in  the  end  to  consider  carefully  at  the  outset  just  what 
data  are  needed.  Where,  as  is  often  the  case,  the  statis- 
tician has  no  control  over  the  collection  of  the  data,  he 

17 


18  STATISTICAL  ARITHMETIC 

» 

should  make  every  possible  attempt  to  ascertain  the  reliabil- 
ity of  the  sources  of  information  and  not  attempt  to  draw 
conclusions  not  warranted  by  the  conditions  under  which 
the  figures  were  collected. 

Statistical  units.  —  The  basic  statistical  process  is  count- 
ing. An  easy  process,  —  one  says ;  and  so  it  is  if  we  know 
what  to  count,  and  if  we  know  what  to  include  and  what  to 
leave  out.  Here  at  the  very  outset  we  meet  our  first  diffi- 
culty. 

Before  going  on  stop  and  define  a  "  dwelling-house." 
Is  a  church  a  dwelling-house  if  the  sexton  lives  in  it?  Is 
a  garage  a  dwelling-house  if  the  chauffeur  lives  in  the  sec- 
ond story?  Is  a  building  with  two  front  doors  one  dwell- 
ing-house or  two?  Is  a  "  three-decker  "  one  dwelling-house 
or  three?  Or  try  to  define  an  infant,  a  birth,  a  cotton-mill 
operative  or  any  other  unit  used  in  demography. 

Statistical  units  are  the  things  counted  and  represented 
by  numbers.  Obviously  every  fact,  every  item,  counted 
must  be  included  within  the  definition  of  the  unit.  No 
part  of  a  statistical  study  demands  more  careful  study  than 
the  definition  of  the  statistical  units  to  be  employed. 
Each  unit  should  not  only  be  rigidly,  accurately  and  in- 
telligibly defined,  it  should  be  steadily  adhered  to  during 
the  investigation.  This  is  by  no  means  easy. 

In  counting  the  number  of  deaths  in  a  city  should  non- 
residents be  included?  Should  still-births  be  included  in 
"births"?  Has  practice  in  this  matter  been  constant 
during  the  last  fifty  years?  Has  pneumonia  always  meant 
what  it  means  to-day?  And  what  has  become  of  the  causes 
of  death  which  no  longer  appear  on  our  lists?  It  is  cer- 
tainly obvious  that  all  statistics  relating  to  the  causes  of 
death  must  be  used  with  the  utmost  caution,  and  this  is 
especially  the  case  if  the  statistics  cover  a  considerable 
period  of  time. 


ERRORS  OF  COLLECTION  19 

Or,  let  us  take  the  simple  matter  of  age.     What  is  a 

seven-year  old  child?     Shall  we  take  the  nearest  birthday, 

(or  the  last  birthday?     Or  shall  we  do  as  is  done  in  some 

foreign  countries  and  take  the  next  birthday?   ^In  the  latter 

lease  a  child  at  birth  is  regarded  as  of  age  one.     Even  the 

i  United  States  census  has  not  always  followed  the  same 

method  of  ascertaining  age. 

Errors  of  collection.  —  One  of  the  errors  of  enumeration 
is  failure  to  find  the  units  to  be  counted.  In  taking  a 
census  some  persons  are  never  found  by  the  enumerators. 
They  may  be  accidentally  missed,  or  they  may  be  traveling, 
away  from  home  or  hiding.  At  the  last  census  in  England, 
where  the  data  are  collected  on  a  single  day,  it  is  said  that 
some  of  the  suffragettes  walked  the  streets  for  the  entire 
period,  so  as  not  to  be  at  home  when  the  enumerators 
called,  arguing  that  if  they  could  not  vote  they  ought  not 
to  be  counted.  Failure  to  obtain  complete  records  is  still 
greater  when  the  data  are  obtained  by  registration. 

The  opposite  error  sometimes  occurs,  namely  over-regis- 
tration. This  is  usually  due  to  carelessness,  but  padded 
censjus  records  have  been  known  to  occur. 

There  are  two  kinds  of  errors  which  need  to  be  distin- 
guished —  balanced  errors  and  unbalanced  errors.  For  ex- 
ample, if  a  thermometer  is  correct  it  may  be  assumed  that  a 
good  observer  will  be  as  likely  to  read  too  high  as  too  low 
and  that  in  a  long  series  of  readings  the  errors  will  balance 
each  other.  But  if  the  thermometer  is  at  fault  all  of  the 
readings  will  be  too  low  or  too  high,  that  is,  the  errors  will 
be  unbalanced.  Causes  of  unbalanced  errors  must  be  re- 
moved if  possible  or,  if  not  removed,  the  results  must  be 
corrected  for  them. 

In  recording  such  quantities  as  the  height  and  weight  of 
persons  the  errors  may  be  regarded  as  balanced,  but  physi- 
cians in  reporting  diseases  may  by  their  practice  of  diagnosis 


20  STATISTICAL  ARITHMETIC 

introduce  unbalanced  errors.  Again,  the  aggregation  of 
the  records  of  various  physicians  may  cause  these  errors  to 
become  more  or  less  balanced. 

Finally  we  have  the  effect  of  the  personal  equation  of  the 
collector.  His  mind  may  have  certain  grooves  through 
which  errors  creep  into  his  work.  If  reading  a  scale  he  may 
have  a  natural  tendency  to  over-estimate  the  space  between 
divisions,  —  if  counting  units  he  may  have  a  natural  tend- 
ency to  skip  some.  What  is  more  serious,  he  may  possess 
the  unpardonable  statistical  sin  of  carelessness,  or  worst  of 
all,  he  may  be  dishonest.  Ignorance  and  failure  to  under- 
stand the  definition  of  the  units  that  are  to  be  enumerated 
are  also  fruitful  sources  of  error. 

Tally  sheets.  —  When  many  items  are  to  be  counted,  and 
especially  when  there  are  different  units  which  must  be 
kept  apart  it  is  convenient  to  use  some  form  of  tally  sheet. 
Each  item  is  first  indicated  by  a  line  or  a  dot  and  these  are 
afterwards  counted.  There  are  two  common  methods  — 
the  cross-five  method  and  the  cross-ten  method.  In  the 
former  every  fifth  item  is  indicated  by  a  line  which  crosses 
four,  making  a  group  of  five.  In  the  latter  nine  items  are 
indicated  by  dots,  the  tenth  by  a  cross  over  the  dots.  Other 
devices  will  doubtless  suggest  themselves  to  the  reader. 
(Fig.  1). 

.  Tabulation.  —  For  purposes  of  study  and  display  the 
collected  data  are  commonly  arranged  in  tabular  form, 
that  is  in  columns  and  lines.  The  preparation  of  tables  is 
ail  important  part  of  statistical  work  and  cannot  be  done 
too  well.  The  object  of  a  table  is  to  bring  statistics  to- 
gether for  comparison,  to  condense  information.  Essential 
qualities  of  good  tabular  work  are  clearness,  compactness 
and  neatness.  Tables  are  expensive  to  print,  hence  the 
most  should  be  made  of  each  one.  The  following  sugges- 
tions, if  followed,  should  yield  good  results: 


TABULATION 


21 


1.  Each  table  should  have  a  title  which  tells  clearly 
what  the  table  contains.  Preferably  the  title  should  be 
short,  but  clearness  is  the  main  thing.  It  is  excellent  train- 
ing in  the  use  of  words  to  produce  an  artistic  title. 


THE  CROSS  FIVE  METHOD 


Disease 

Number 

Measles 

UM  ////  ////  //                     /7 

Scarlet-fever 

UM  ///                                    8 

Whooping-cough 

////  ////  ////  ////                 2O 

THE  CROSS  TEN-METHOD 


Disease 

Ja 

n. 

JbY 

b. 

Me 

ir. 

AF 

>r. 

M 

ij' 

Ju 

nc 

Et 

c. 

Measles 

!  i 

5 

5 

/. 

•^ 

f- 

•^ 

> 

f 

Scarlet-fever 

'/ 

I 

/ 

f 

•  ; 

*' 

•^ 

?\ 

c 

) 

5 

*r 

sc 

* 

I" 

•  .  . 

^ 

::: 

^. 

^' 

::: 

2 

0 

/ 

^ 

^ 

/ 

7 

•)fe 

^< 

^ 

s 

FIG.  1.  — Tally  Sheets. 

2.  Each  column  should  have  a  clear  and  appropriate 
heading.     As  the  space  for  the  heading  is  often  small  ab- 
breviations may  be  used,  provided  they  are  well  understood 
or  well  explained  in  the  accompanying  text. 

3.  If  the  heading  is  complex,  that  is,  if  certain  parts  of 
the  heading  cover  more  than  one  column,  care  should  be 
taken   to  have   this   clearly   indicated  by  proper   rulings. 


22  STATISTICAL  ARITHMETIC 

Printers  call  this  "  boxing."     If  there  are  few  columns  and  if 
the  headings  are  simple,  the  rulings  are  unnecessary. 

4.  If  the  different  columns  of  a  table  are  likely  to  be  re- 
ferred to  in  the  text  it  is  convenient  to  have  each  column 
given  a  serial  number  from  left  to  right,  placed  in  paren- 
thesis just  below  the  heading. 

5.  Long  unbroken  columns  of  figures  are  confusing  to  the 
eye;   especially  if  the  figures  of  different  columns  are  to  be 
compared  on  a  given  line.     This  trouble  can  be  obviated  by 
leaving  horizontal  spaces  between  every  few  lines  or  by  the 
use    of    horizontal    rulings.     Sometimes,    for   purposes   of 
reference,  each  line  is  given  a  serial  number  from  top  to 
bottom. 

6.  The  columns  of  a  table  should  not  be  widely  separ- 
ated even  if  there  are  only  a  few  columns  and  the  page  is 
large.     Compactness  is  a  virtue.     Much  paper  is  wasted  in 
annual  reports  by  badly  arranged  tables.     On  the  other 
hand  the  type  used  in  tabular  work  should  not  be  too 
small. 

7.  If  the  figures  tabulated  have  more  than  three  signifi- 
cant figures  it  is  a  good  plan  to  separate  them  into  groups 
of  three.     Thus,  we  should  not  write  6457102,  but  6  457  102. 

Tables  1  and  2  are  given  as  examples  of  tabulation  and 
boxing.  From  this  point  on  students  should  criticize  the 
tables  in  this  book  (a  few  of  which  have  been  intentionally 
made  imperfect),  and  they  should  use  great  care  in  the  prep- 
aration of  every  table  involved  in  the  "  Exercises  and  Ques- 
tions." 


TABULATION 


23 


TABLE  1 

CAMBRIDGE,  MASS. 
Estimates  of  Population 


Year. 

Census. 

Estimate 
based  on 
U.S. 
census. 

Estimate 
based  on 
U.  S.  and  state 
census. 

Estimate 
based  on 
local  data. 

Estimate 
used  by 
local  board 
of  health. 

Estimate 
used  in 
this  report. 

(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

(7) 

1890 

1 

2 

4 

5 

G 

7 

8 

9 

1900 

1 

2 

3 

4 

5 

6 

7 

8 

9 

• 

1910 

11 

12 

13 

14 

15 

16 

17 

18 

24 


STATISTICAL  ARITHMETIC 


TABLE  2 
CAMBRIDGE,  MASS.:  BIRTH-RATES 


Year. 

Population 
estimate. 

Number  of  Births. 

Birth-rate. 

Total. 

Resident. 

Gross. 

Resident. 

As  stated 
by,  etc. 

(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

(7) 

Inexact  numbers.  —  In  vital  statistics  we  are  usually 
compelled  to  deal  with  data l  which  are  not  strictly  accurate. 
The  figures  used  to  express  the  results,  therefore,  should  bo 
prepared  with  this  fact  in  mind.  Unnecessary  figures 
should  be  omitted  and  only  those  digits  should  be  included 
which  are  supported  by  the  data.  Two  guiding  principles 
should  be  followed  in  making  numerical  statements  of 
data;  —  first,  to  have  the  figures  of  the  compilation  depend 
upon  and  indicate  the  accuracy  of  the  observations;  and, 
second,  to  carry  the  final  numerical  result  no  further  than 
practical  use  demands. 

Let  us  take  as  an  illustration  the  result  of  the  U.  S. 
Census  of  1910,  according  to  which  the  population  of  the 

1  Do  not  misuse  this  word.  It  is  a  plural  word.  The  singular  num- 
ber is  "datum,"  but  this  is  seldom  used.  Do  not  say,  "The  data 
is  .  .  "  but  "The  data  are.  .  .  ." 


INEXACT  NUMBERS  25 

Country  is  stated  as  91,972,266.  Obviously  this  figure 
mnnot  be  strictly  true.  Let  us  suppose  the  possible  error 
:o  be  as  much  as  200,000.  We  might  write  the  result  "  92 
million";  but  this  would  be  needlessly  crude,  though  accu- 
rate enough  for  some  purposes.  We  might  say  that  the 
population  was  between  91.8  and  92.2  million,  or  we 
might  write  92,000,000  ±  0.2  per  cent.  The  U.  S.  Census 
Bureau  publishes  the  figures  as  collected,  leaving  it  for 
him  who  uses  the  figures  to  abbreviate  them  into  round 
numbers  according  to  the  use  which  is  to  be  made  of 
them. 

Experience  has  shown  that  very  few  measurements  or 
observations  of  anything  are  accurate  to  five  significant 
figures,  many  not  to  three,  and  some  are  doubtful  in  the 
second  figure. 

In  tabulating  the  results  of  original  data  it  is  best  to  give 
the  figures  as  obtained.  But  in  discussing  the  results  it  is 
better  to  use  round  numbers,  the  number  of  significant 
figures  depending  on  the  accuracy  of  the  data  and  the  needs 
of  the  problem  at  hand. 

In  presenting  figures  orally  to  an  audience  it  is  especially 
important  to  use  round  numbers.  Nothing  is  more  dead- 
ening than  for  a  speaker  to  tire  the  ear  with  the  reiteration 
of  meaningless  digits. 

Example.  —  Let  us  suppose  that  the  number  of  bacteria 
on  a  plate  can  be  counted  within  five  per  cent,  plus  or  minus, 
and  that  three  different  tests  gave  the  following  numbers: 
-  2790,  4220  and  3470  per  c.c.  the  average  being  3493. 
Five  per  cent  of  this  figure  is  175;  —  hence  the  true  result 
might  conceivably  lie  between  3318  and  3668.  Obviously 
it  would  be  sufficiently  accurate  and  for  many  reasons 
better  to  state  the  result  as  3500  per  c.c.  Recognizing  these 
unavoidable  errors  in  our  present  methods  the  Committee 
on  Standard  Methods  of  Water  Analysis  of  the  American 


26 


STATISTICAL  ARITHMETIC 


Public  Health  Association  has  suggested  that  statements  oi 
analysis  should  be  limited  in  significant  figures  as  follows 
Unfortunately  the  rule  has  not  been  lived  up  to. 

TABLE  3 

RULE  FOR  STATING  THE  RESULTS  OF  BACTERIAL 
COUNTS  IN  WATER  ANALYSIS 


Numbers  of  bacteria  found. 

Records  to  be  made. 

1  to               50 

As  found 

51  to             100 

To  the  nearest            5 

101  to             250 

' 

10 

251  to             500 

25 

501  to          1,000 

< 

50 

1,001  to         10,000 

< 

100 

10,001  to        50,000 

500 

50,001  to       100,000 

1,000 

100,001  to       500,000 

10,000 

500,001  to    1,000,000 

50,000 

1,000,001  to  10,000,000 

100,000 

Perhaps,  sometime,  demographers  will  prepare  a  similar 
table  for  the  use  of  round  numbers  in  vital  statistics. 

Vital  statisticians  should  at  least  endeavor  to  follow  the 
example  of  the  bacteriologists  and  by  concerted  action  cut 
out  fictitious  accuracy  from  their  reports. 

Precision  and  accuracy.  —  Numerical  statements  of 
measurements  are  accurate  as  they  approach  the  true  value 
of  the  thing  measured;  they  are  precise  as  they  approach 
the  mean  of  the  measurements.  Accuracy  takes  into  ac- 
count unbalanced  as  well  as  balanced  errors;  precision  is 
concerned  with  balanced  errors  only.  It  is  possible  for 
results  to  be  precise  and  yet  be  erroneous. 

Combinations  of  inexact  numbers.  —  When  data  which 
differ  in  precision  are  combined  it  is  possible  that  faults 
may  be  obscured.  Let  us  take  the  case  of  a  simple  addi- 
tion of  the  three  items  in  column  (1). 


RATIOS 


27 


TABLE  4 
EXAMPLE  OF  COMBINATION  OF  INEXACT  NUMBERS 


Item. 

Percentage  error. 

Possible  error  in  item. 

(1) 

(2) 

(3) 

47,386  - 
9,453 

843,782 

2 
5 
0.5 

±   948 

db  473 
±4219 

Sum    900,621 

±5640,  or  0.6% 

The  true  value  of  the  sum  may  lie  between  895,000  and 
906,000.  The  result  may  be  written,  therefore,  900,000 
±  0.6  per  cent.  The  percentage  error  of  the  sum  would 
not,  of  course,  be  the  sum  or  even  the  average  of  the  figures 
in  the  second  column. 

Ratios.  —  The  ratio  between  two  numbers  may  be  ex- 
pressed as  a  common  fraction  or  may  be  indicated  by  the 
ratio  symbol,  the  colon  (:).  Thus  we  may  write  f  or  4  :  8. 
If  the  figures  are  small  the  difference  between  the  two  num- 
bers can  be  visualized,  but  if  they  are  large,  as  for  example 
iff,  or  165  :  217,  it  is  difficult  to  appreciate  their  meaning. 
If  common  fractions  are  used  to  indicate  ratios  they  should 
be  limited  to  those  in  which  the  denominator  is  below  10, 
or  is  some  round  number,  such  as  a  multiple  of  5  or  10. 
Thus  we  might  speak  understandingly  of  a  J  or  a  J  or  a  ^  or 
a  rnv,  but  not  of  a  ^  or  a  ^. 

For  most  purposes  in  statistical  work  decimal  fractions  are 
to  be  preferred  to  common  fractions.  They  facilitate  print- 
ing as  they  occupy  only  one  line  and  do  not  require  the  use 
of  smaller  type.  It  must  never  be  forgotten,  however,  that 
a  decimal  fraction  is  composed  of  two  parts,  just  as  a  com- 
mon fraction,  namely  the  figures  which  are  printed  and 


STATISTICAL  ARITHMETIC 


unity  (or  one)  which  is  not  printed. 


„,       3      0.75 

Thus  j  =  — r—  =  0.75. 

A  decimal  fraction  is  therefore  just  as  much  a  ratio  as  a 
common  fraction. 

In  statistical  work  we  are  constantly  obliged  to  compare 
facts  on  the  basis  of  their  ratios.  Let  us  suppose  that  we 
desire  to  compare  cases  and  deaths  from  typhoid  fever  in 
three  different  places  and  that  the  data  are  as  follows: 


TABLE  5 


Place. 

Cases. 

Deaths. 

(1) 

(2) 

(3) 

X 

541 

46 

Y 

672 

53 

Z 

247 

30 

In  order  to  make  the  comparison  we  must  select  either  one 
or  the  other  quantity  as  a  base,  either  cases  or  deaths. 
If  we  select  one  death  as  the  unit  base  we  have  the  following 
ratios : 

TABLE  6 


Place. 

Number  of  cases  to  one  death. 

(1) 

(2) 

X 
Y 
Z 

11.8  i.t 
12.7 
8.2 

5.  541  -J-  46 
672  4-  53 
247  ^  30 

If  we  select  one  case  as  the  unit  base  we  have  the  follow- 
ing ratios,  expressed  as  decimals: 


RATES 


29 


TABLE  7 


Place. 

Number  of  deaths  to  one  case. 

(1) 

(2) 

X 
Y 
Z 

0.085 
0.079 
0.121 

i.e.  46-7-541 
53-:-  672 

30  -T-  247 

We  might  however  select  100  cases  as  the  base  unit,  in 
which  case  the  figures  are  100  times  as  large  and  we  have 

TABLE  8 


Per  cent  of 

Place. 

cases  which 
resulted  in 

death 

(1) 

(2) 

X 

8.5 

Y 

7.9 

Z 

12.1 

Rates.  —  Now  rates  are  merely  ratios  referred  to  some 
round  number  as  a  base.  When  100  is  used  as  the  base  we 
have  a  percentage  rate,  that  is  a  rate  per  one  hundred; 
but  we  may  use  10  or  10,000  or  even  100,000  or  1,000,000' 
as  the  base,  and  very  often  do  so.  In  many  cases  we  use 
one  as  the  base.  Thus  we  speak  of  "  gallons  of  water  per 
day,"  meaning  the  number  of  gallons  of  water  fpr  one  day, 
the  "number  of  persons  per  square  mile,"  meaning,  of  course, 
one  square  mile.  All  of  these  rates,  where  only  two  quan- 
tities are  compared  may  be  called  simple  rates.  Simple 
rates  have  only  one  base. 

Compound  rates  are  those  which  have  two  bases.  Thus 
we  speak  of  "  gallons  of  water  per  capita  per  day,"  meaning 


30  STATISTICAL  ARITHMETIC 

the  number  of  gallons  of  water  used  by  one  person  in  one 
day.  The  "  number  of  births  per  1000  marriages  per 
annum  "  would  also  be  a  compound  rate.  Most  of  the 
rates  used  for  comparison  in  vital  statistics  are  compound 
rates  as  they  involve  both  number  and  time,  the  latter 
often  being  understood  as  one  year,  the  calendar  year  per- 
haps. 

Misuse  of  rates.  —  Fictitious  accuracy  in  the  use  of 
rates  and  ratios  should  be  avoided.  If  35  out  of  57  balls 
were  white  the  percentage  of  white  balls  would  be  61  404 
per  cent.  The  smallest  possible  error,  i.e.,  1,  would  change 
the  percentage  to  59.65  per  cent  or  63.16  per  cent.  To  use 
two  or  even  one  place  of  decimals  is  here  absurd.  Clearly 
for  figures  less  than  100  fractions  of  per  cents  are  illogical. 
In  the  same  way  death-rates  for  populations  of  less  than 
1000  are  useless  beyond  the  third  significant  figure.  Com- 
parisons of  averages  of  fictitious  values  are  also  to  be  avoided. 

Changes  of  base  in  the  computation  of  rates  should  be 
kept  in  mind  in  order  to  avoid  error  of  statement.  Here 
is  a  well-known  illustration:  In  the  year  1880  the  receipts 
of  a  water  company  were  $400,000;  between  1880  and  1890 
they  increased  10  per  cent,  that  is,  they  became  $440,000; 
between  1890  and  1900  they  decreased  10  per  cent,  that  is, 
they  became  $396,000  (not  $400,000).  It  is  said  that  a 
strike  once  resulted  from  this  fallacy.  A  company  found  it 
necessary  to  reduce  wages  20  per  cent  for  a  certain  period, 
promising  to  raise  the  wages  20  per  cent  at  the  end  of  the 
period.  Naturally  the  men  who  were  reduced  from  $2.00 
a  day  to  $1.60  thought  they  would  have  their  pay  restored 
to  $2.00  but  found  that  the  company  wished  to  give  only 
$1.60  +  20  per  cent  or  $1.92.  The  base  used  should  be 
stated  in  words  if  it  is  not  perfectly  clear  from  the  context. 

When  interpreting  ratios  it  should  be  carefully  noted 
whether  or  not  the  numerator  bears  a  direct  relation  to  the 


INDEX  31 

lenominator.  In  proportion  as  it  fails  to  do  so  any  infer- 
mce  from  it  is  less  valuable.  The  ratio  between  the  num- 
>er  of  births  and  the  total  population  is  less  close  than  that 
>etween  the  number  of  births  and  the  number  of  married 
vomen  of  child-bearing  age. 

Ratios  are  sometimes  necessarily  used  in  an  indirect  way. 
Fhus  the  average  annual  exports  and  imports  are  taken  to 
•epresent  the  business  condition  of  a  country.  Here,  a 
mrt  is  taken  for  the  whole.  The  method  is  proper  if,  in 
-he  interpretation,  it  is  recognized  that  it  is  a  part.  Or  the 
yphoid  fever  death-rate  of  a  city  is  taken  as  an  index  of 
;he  sanitary  quality  of  the  public  water  supply.  It  may 
ndeed  be  such  an  index,  but  it  is  not  the  only  one. 

In  the  same  way  crude  death-rates  based  on  total  popu- 
ation  regardless  of  sex  or  age  are  less  useful  in  studying 
•elative  hygienic  conditions  than  when  these  factors  are 
:aken  into  account. 

Index.  —  When  it  is  not  possible  to  find  a  simple  direct 
*atio  between  two  quantities,  it  is  sometimes  possible  to 
Combine  several  ratios  which  taken  together  give  a  better 
ndication  of  the  conditions  than  any  one  ratio  used  alone, 
rhus  the  prices  of  various  standard  commodities  sold  in 
my  one  year  may  be  combined  to  give  a  single  figure  which 
,dll  indicate  the  state-  of  trade  during  that  year.  This 
combined  result  compared  with  a  similar  result  for  the 
Allowing  year  will  enable  one  to  compare  the  state  of  trade 
n  the  two  years.  When  several  quantities  are  thus  com- 
bined the  result  is  called  an  Index,  or  an  Average  Index. 
Dbviously  there  are  various  ways  in  which  a  combination 
nay  be  made.  Sometimes  the  weighted  average  of  several 
quantities  is  used. 

The  index  has  not  come  into  use  to  any  extent  in  the 
study  of  vital  statistics,  but  it  would  seem  logical  to  use  it 
in  comparing  the  relative  hygienic  conditions  of  different 


32  STATISTICAL  ARITHMETIC 

cities.  This  is  partially  accomplished  when  crude  deaths 
rates  are  "  corrected "  or  adjusted  to  take  into  accoun 
the  composition  of  population  as  to  age,  sex  and  natior 
ality. 

Some  attempts  to  compute  a  satisfactory  sanitaiy  inde 
will  be  referred  to  later  on. 

Computation  of  Rates.  —  The  computation  of  a  deatl: 
rate  for  a  city  is  merely  an  example  in  long  division.  A 
most  health  officials  and  some  college  students  will  hav 
forgotten  their  arithmetic  by  the  time  they  read  this  boo 
a  few  words  as  to  computation  may  be  pardoned.  Th 
computation  sheet  should  show  a  record  of  what  has  bee 
done  and  should  bear  the  date  and  the  name  or  initials  ( 
the  computer. 

Let  us  suppose  that  in  a  city  of  34,691  people,  as  show 
by  the  census  of  1910,  the  number  of  deaths  in  that  year  w£ 
549;  what  was  the  death-rate  per  thousand  of  population 
In  the  first  place  how  many  thousands  of  population  wei 
there?  Answer,  by  pointing  off  three  places,  34.691.  A 
that  is  necessary  then  is  to  divide  549  by  34.691.  Th 
may  be  done  in  several  ways 

The  operation  of  long  division  may  be  done  in  full,  thus 

34.691)549.000(15.82  =  death-rate  per  1000. 
34691 
202090 
173455 


286350 

277528 
88220 
69382 


.If  we  are  content  to  be  a  little  less  accurate  we  ma 
shorten  the  work  by  leaving  off  one  decimal  of  the  popuk 
tion,  thus: 


COMPUTATION  OF  RATES  33 

34.69)549.00(15.82  =  Answer 
3469 
20210 
17345 


28650 
27752 
8980 
6938 


The  result  is  not  changed.     If  we  write  34.7  instead  of  34.69 
we  shall  get 

34.7)549.0(15.82  =  Answer 
347 
2020 
1735 


2850 
2776 

740 

694 

Still  no  change.  Suppose  we  try  35  as  a  round  number 
for  the  population  instead  of  34.7  or  34.69  or  34.691.  We 
then  get 

35)549(15.7  =  Answer 

35_ 

199 

175 
240 
245 

This  is  evidently  incorrect  in  the  decimal.  We  have  gone 
too  far  in  using  a  round  number  for  the  population. 

By  using  discretion  in  omitting  decimals  from  the  popu- 
lation divisor  much  work  may  be  saved.  It  is  pitiful  to  see 
the  energy  and  time  wasted  by  some  health  officers  in  using 
unnecessary  decimals  in  performing  long-division  opera- 
tions, especially  as  there  are  so  many  labor-saving  devices 


IT 


34  STATISTICAL  ARITHMETIC 

available.  An  easier  way  is  to  use  a  table  of  logarithms, 
and  a  still  easier  way  is  to  use  a  slide-rule,  a  mechanical 
device  for  applying  logarithms  where  approximate  results 
will  suffice. 

The  desirable  degree  of  accuracy  of  death-rates  is  dis- 
cussed on  a  later  page. 

Logarithms.  —  Of  course  you  have  forgotten  how  to  use 
logarithms.  Let  me  remind  you. 

If  you  multiply  10  by  10  you  get  100.  You  have  put 
two  tens  together,  and  you  might  write  them  thus  102  and 
say  that  102  =  100.  If  you  put  three  tens  together  you 
get  1000.  So  that  103  =  1000.  And  so  on.  Now,  ten  is 
the  base  of  logarithms,  and  we  say  that  the  log  (meaning 
logarithm)  of  100  is  2,  because  2  tens  multiplied  together 
makes  100.  And  the  log  of  1000  is  3  and  the  log  of  1,000,000 
is  6.  So  also  the  log  of  10  is  1,  the  log  of  1  is  0,  and  the  log 
of  0.1  is  minus  1,  i.e.,  —  1,  and  so  on  down.  Now  if  the 
log  of  10  is  1  and  the  log  of  100  is  2,  what  is  the  log  of  20? 
It  is  between  1  and  2;  it 'is  1  plus  something.  Just  what 
this  something  is  you  can  find  from  a  table  of  logarithms. 
A  short  table  (five  places)  gives  for  the  log  of  2  the  figures 
.30103,  so  that  the  log  of  20  is  1  plus  .30103,  or  1.30103.  In 
the  same  way  the  log  of  200  is  between  2  and  3;  in  fact 
it  is  2.30103.  And  so  we  can  find  the  logarithm  of  any 
number,  taking  the  decimal  from  the  printed  table,  and 
putting  down  the  figure  to  the  left  of  the  decimal  point 
according  to  the  size  of  the  original  figure,  remembering 
that  for  figures 

Between        0   and         10,  the  log  is  0 

10     "          100,        "         1 

100     "        1000,        "         2 

1000  "    10,000,        "         3.. 


THE  SLIDE-RULE  35 

We  use  those  logarithms  iri  this  way.  Suppose  we  wish 
to  multiply  100  X  10,000.  We  might  do  this  in  the 

regular  way, 

10,000 
100 
1,000,000  =  Answer. 

But  the  log  of  100  is  2  and  the  log  of  10,000  is  4.  If  we 
add  these  logarithms  we  get  6,  and  6  is  the  log  of  our  answer. 
That  is  by  adding  the  logs  of  two  number,  the  sum  will  be 
the  log  of  the  product  of  the  numbers. 

And  also  if  we  subtract  the  log  of  one  number  from  the 
log  of  another  the  difference  will  be  the  log  of  the  dividend 
obtained  by  dividing  the  second  number  by  the  first.  Thus 
in  our  death-rate  problem  the  log  of  549  is  2.739572  and 
the  log  of  34.691  is  1.540216.  Hence, 

2.73957 
1.54022 
1.19935  is  the  log  of  15.82  =  the  answer. 

It  must  be  remembered  that  the  logarithm  table  contains 
only  the  decimals.  That  is  we  look  up  the  number  which 
corresponds  to  the  decimal  .199356  and  find  the  figures  to 
be  1582.  The  whole  number  of  the  log  being  1  tells  us  that 
the  result  is  between  10  and  100,  and  therefore  must  be 
15.82. 

In  this  way  the  use  of  logarithms  may  save  the  statis- 
tician much  time. 

A  table  of  logarithms  of  numbers  from  1  to  1000,  carried 
to  five  decimal  places,  may  be  found  in  the  Appendix. 
Tables  in  which  there  are  six  or  seven  places  of  decimals 
can  be  purchased  and  are  in  common  use. 

Those  who  do  not  feel  confidence  in  themselves  in  using 
logarithms  should  consult  a  textbook  of  algebra. 

The  slide-rule.  —  The  slide-rule  is  a  mechanical  device 
for  adding  and  subtracting  the  logarithms  of  numbers, 


36 


STATISTICAL  ARITHMETIC 


and  therefore  it  enables  one  to  multiply  the  numbers  for 
which  the  logarithms  stand.  It  does  not  add  or  subtract 
the  numbers  themselves. 

In  using  the  slide-rule  it  is  first  necessary  to  understand 
the  scale.  The  logarithms  of  the  numbers  from  1  to  10  are 
as  follows: 

TABLE  9 
LOGARITHMS  OF  NUMBERS:    1  TO  10 


Number. 

Logarithm. 

Number. 

Logarithm. 

(1) 

(2) 

(3) 

(4) 

1 

0.00000 

6 

0.77815 

2 

0.30103 

7 

0.84510 

3 

0.47712 

8 

0.90309 

4 

0.60206 

9 

0.95424 

5 

0.69897 

10 

1.00000 

and  above  10  the  decimals  repeat  themselves,  thus 


20 
30 


1.30103 
1.47712 


etc. 

If  these  are  plotted  on  a  uniform  scale  we  get  the  result 
shown  in  Fig.  2A.  •  It  will  be  noticed  that  on  the  number 
scale  the  divisions  grow  smaller  as  the  numbers  increase. 
It  is  this  number  scale  which  appears  on  the  slide  rule. 
There  are  many  subdivisions.  The  space  from  1  to  2  is 
divided  into  10  parts,  and  so  are  the  other  spaces.  The 
space  between  1  and  1.1  is  also  divided  into  ten  parts; 
but  above  2  there  is  not  room  for  so  many  lines,  so  the 
values  of  the  divisions  change  and  one  must  be  on  his 
guard  not  to  make  an  error  in  scale  reading.  It  should 
be  remembered  that  just  as  the  main  divisions  be- 
tween 1  and  10  are  unequal,  so  are  the  subdivisions  be- 


THE  SLIDE-RULE 


37 


CD 


38  STATISTICAL  ARITHMETIC 

tween  1  and  2  unequal.  The  minor  subdivisions  are  also 
unequal  but  the  eye  cannot  distinguish  these  small  differ- 
ences. 

Let  us  first  learn  how  to  multiply  two  numbers  —  say 
multiply  2  by  4.  We  use  the  lower  scale  on  the  slide  and 
the  lower  scale  on  the  rule  under  it.  The  two  scales  are 
just  alike.  If  the  left-hand  end  of  the  slide  is  set  on  2  of 
the  rule,  then  the  distance  (a)  along  the  slide  is  the  log  of  2, 
and  the  distance  (6)  along  the  slide  is  the  log  of  4.  The 
sum  of  (a)  and  (6),  i.e.,  (c)  is  the  sum  of  the  logs  of  2  and  4 
and  therefore  is  the  log  of  their  product.  And  so  we  find 
that  the  distance  (c)  from  the  end  of  the  rule  gives  us  8,  the 
result,  under  the  figure  4  of  the  slide. 

Suppose,  however,  that  we  want  to  multiply  2  by  6.  The 
distance  (c)  would  then  extend  to  6  on  the  slide,  or  beyond 
the  scale  of  the  rule.  That  is  the  product  is  more  than  10. 
Remembering  that  the  log  numbers  repeat  themselves  above 
10,  all  we  have  to  do  is  to  set  the  right-hand  instead  of  .the 
left-hand  end  of  the  slide  on  the  figure  2,  of  the  rule  and 
then  read  on  the  rule]the  number  under  6  of  the  slide.  It  is  12. 

The  process  of  division  is  just  the  reverse  of  that  of  mul- 
tiplication. To  divide  8  by  4,  set  4  of  the  slide  over  8  of 
the  rule  and  read  1  (the  end)  of  the  slide  on  the  rule  (i.e.,  2). 

The  upper  marks  on  the  ordinary  slide  and  rule  are  not 
needed  for  simple  multiplication  and  division.  The 
movable  wire  is  used  as  a  guide  and  reference  mark. 

To  return  to  our  death-rate  problem  (above)  we  may 
divide  549  by  34.69  by  setting  3469  on  the  slide  over  549  of 
the  rule  and  reading  1  of  the  slide  on  the  lower  scale  of  the 
rule.  The  result  is  158+  as  before.  It  is  difficult  to  set 
3469  exactly,  so  it  is  impossibly  to  read  the  result  to  more 
than  three  significant  figures. 

The  slide-rule  does  not  give  us  the  decimal  points.  That 
had  best  be  determined  by  inspection.  (There  are  indeed 


CLASSES,   GROUPS,   SERIES  AND  ARRAYS  39 

rules  for  the  decimal  point,  but  they  are  hard  to  remember 
and  one  should  not  attempt  to  do  so.)  Inspection  shows 
that  34  goes  in  549  more  than  10  and  less  than  20  times; 
consequently  the  slide-rule  result  is  15. 8+ . 

Slide-rules  are  made  in  many  different  lengths,  from  three 
or  four  inches  up  to  twenty  inches.  A  ten-inch  rule  is  best 
for  general  use.  The  twenty-inch  rule  is  easier  on  the  eyes 
and  can  be  read  closer,  but  it  cannot  be  carried  in  the  pocket. 
Celluloid  rules  are  the  best,  as  the  marks  are  clear,  but 
cheap  wooden  rules  are  satisfactory  for  some  purposes. 

Books  of  instruction  accompany  most  of  the  high-grade 
rules  and  can  always  be  purchased. 

Every  statistician  ought  to  know  how  to  use  logarithms 
and  how  to  read  a  slide-rule.  Life  is  too  short  and  time 
nowadays  is  too  precious  to  depend  upon  the  old  methods  of 
long  division  and  multiplication  if  much  work  is  to  be  done. 

Classification  and  generalization.  —  For  purposes  of 
study  it  is  usually  necessary  to  sort  out  the  various  data, 
divide  them  up  into  classes,  groups  or  series  and  to  make 
generalizations  in  various  ways.  Some  of  these  processes 
are  very  simple;  others  are  rather  complicated.  The 
methods  used  vary  according  to  the  nature  of  the  problem 
at  hand.  As  far  as  possible  the  simple  methods  should  be 
preferred  to  the  more  complex  procedures. 

Classes,  groups,  series  and  arrays.  —  Collections  of  units 
which  differ  from  other  collections  by  characteristics  which 
cannot  be  expressed  in"  figures  are  properly  termed  sections 
or  classes.  Thus,  populations  are  divided  into  classes  ac- 
cording to  sex,  nationality,  conjugal  condition,  civil  divisions. 

Collections  of  units  which  differ  from  other  collections  by 
characteristics  which  can  be  expressed  in  figures  are  called 
groups.1  As  an  example  populations  are  divided  into  age 

1  This  distinction  is  not  universally  made,  but  if  rigidly  adhered  to 
it  would  result  in  greater  clearness  of  expression. 


40  STATISTICAL  ARITHMETIC 

groups,  or  into  groups  of  persons  having  different  weights  or 
heights. 

Data  are  also  arranged  in  series  according  to  some  natural 
sequence  or  some  order  of  magnitude  or  chronological  order. 
When  all  of  the  items  of  a  given  group  are  arranged  in  order 
of  magnitude  from  small  to  large,  or  large  to  small,  they  are 
said  to  be  placed  in  array.  Companies  of  soldiers  arranged 
with  the  tallest  man  at  one  end  of  a  rank  and  grading  down 
to  the  smallest  man  at  the  other  end  form  an  array. 

Classes  of  data.  —  Little  need  be  said  about  classification 
except  that  the  definitions  of  classes  should  be  clearly  and 
accurately  stated,  and  so  drawn  as  to  be  mutually  exclusive, 
that  is,  it  should  not  be  possible  for  an  item  to  appear  in 
more  than  one  class. 

Generalization  of  classes  and  groups.  —  The  average, 
although  a  convenient  device  for  generalizing  the  facts  in  a 
class  or  in  a  group  of  observations,  has  a  number  of  short- 
comings. It  does  not  give  a  true  picture  of  the  different 
items.  Two  groups  may  have  the  same  average  and  yet 
be  composed  of  very  different  items.  Thus: 

6  1 

6  1 

7  2 
7  3 

_2  ?? 

Sum         35  35 

Average     7  7 

In  a  large  number  of  items  there  may  be  one  important 
item  of  large  magnitude  which  might  be  concealed  by  the 
average.  On  the  other  hand  a  large  item,  if  erroneous, 
might  unduly  raise  the  average  and  give  a  false  generali- 
zation. Another  name  for  the  average  is  the  .mean. 

Some  other  forms  of  generalization,  therefore,  are  neces- 
sary in  statistical  work. 


THE  ARRAY  AND   ITS  ANALYSIS 


41 


The  array  and  its  analysis.  —  If  the  items  are  arranged  in 
order  of  magnitude  with  the  smallest  at  one  end  and  the 
largest  at  the  other  they  are  said  to  be  in  array.  If  the 
number  of  items  is  not  too  great  this  gives  an  excellent 
picture  of  the  group.  Thus  Fig.  3  shows  at  a  glance  that 
the  two  groups  on  page  40  are  different  from  each  other. 


30 


fso 


10 


Average  -7 


FIG.  3.  —  Example  of  Differing  Groups  which  have  the  Same  Average. 

In  an  array  the  magnitude  of  the  middle  item  is  called  the 
median.  This  is  a  very  important  unit  in  statistical  analy- 
sis. The  means  are  the  same  for  the  above-mentioned 
groups,  i.e.,  7,  but  the  medians  are  different,  i.e.,  7  and 
2.  The  median  may  be  the  same  as  the  mean,  —  in  fact, 
it  usually  is  near  the  mean,  —  but  it  need  not  be  the  same. 

The  mode  is  the  magnitude  of  the  item  which  is  most 
common  among  the  items.  A  modish  bonnet  is  one  very 
commonly  seen;  it  is  the  fashionable  one.  In  one  of  our 
two  groups  there  are  two  sixes  and  two  sevens  and  we 


42 


STATISTICAL  ARITHMETIC 


cannot  tell  which  is  the  mode.     They  are  tied  for  first  place. 
In  the  other  group  the  mode  is  clearly  one. 

The  magnitude  of;  the  item  halfway  between  the  median 
and  the  upper  limit  is  called  the  upper  quartile,  and  the 
corresponding  item  towards  the  lower  end,  the  lower 
quartile:  A  quartile  is  one-quarter  of  the  way  from  one 
end  of  the  array  to  the  other.  See  Fig.  4. 


15 


M 


Mean  =  7.28 


' 


P  '  I  II 


FIG.  4.  —  An  Array  of  Observations. 

The  magnitude  of  the  item  one-tenth  of  the  way  from 
the  lower  to  the  upper  limit  of  the  array  is  the  lower  decen- 
tile.  And  so  there  may  be  quintiles,  and  other  "  iles." 

These  various  units  help  very  much  to  give  one  a  picture 
of  an  array.  They  are  used  in  various  combinations,  and 
ratios  are  made  up  by  using  them. 

The  average,  together  with  the  maximum  and  minimum, 
offers  a  common  form  of  generalization.  The  median, 


GROUPS  43 

together  with  the  upper  and  lower  decentiles,  is  sometimes 
used.  The  quartile  difference,  that  is  the  difference  be- 
tween the  two  quartiles,  is  used. 

Again  the  ratio  of  the  maximum  (or  minimum)  to  the 
mean,  the  ratio  of  the  quartiles  to  the  median,  the  ratio  of 
the  mean  to  the  median,  and  other  ratios  have  been  used. 

Still  another  way  is  to  find  the  extent  to  which  the  differ- 
ent items  differ  from  the  mean  and  study  these  differences. 

This  subject,  which  involves  such  matters  as  variation, 
dispersion  and  the  like,  takes  us  into  the  very  heart  of  the 
statistical  method  and  will  be  treated  at  length  in  Chapter 
XII. 

Groups.  —  The  problem  of  arranging  statistical  data 
into  groups  is  a  troublesome  one,  —  troublesome  because 
there  are  several  ways  in  which  groups  can  be  made  and 
defined. 

Let  us  take  the  case  of  nine  persons  whose  illness  from 
a  certain  disease  lasted  respectively  13,  11,  6,  9,  12,  10,  8,  17 
and  13  days.  We  will  consider  these  merely  as  whole 
numbers  and  try  to  arrange  them  in  groups.  A  common 
way  would  be: 

(1)          (2)  (3)  (4) 

Days 0-5        5-10  10-15        15-20 

Number  of  persons     0          4  (or  3?)       4  (or  5?)        1 

There  is  confusion  here  because  one  does  not  know 
whether  to  put  the  item  10  into  the  second  or  third  group. 
The  groups  are  not  clearly  stated.  They  are  not  mutually 
exclusive. 

Another  way  would  be  to  arrange  the  groups  thus,  making 
the  upper  and  lower  limits  both  inclusive. 

(1)         (2)  (3)  (4)  (5) 

Days 0         1-5        6-10        11-15        16-20 

Number .  .  .0  0  -  4  4  1 


44  STATISTICAL  ARITHMETIC 

A  better  way  would  be  this: 

(1)          (2)  (3)  (4) 

Days 0-4        5-9        10-14        15-19 

Number 035  1 

The  last  two  methods  are  both  used.  The  means  for  the 
four  groups  in  the  last  method  would  be  respectively  2 
(average  of  0  to  4),  7,  12  and  17.  The  means  for  the  five 
groups  in  the  next  to  the  last  method  would  be  0,  3,  8,  13 
and  18. 

Let  us  next  take  a  case  where  we  have  to  deal  with  whole 
numbers  and  fractions,  —  say  to  the  nearest  quarter,  — 
and  where  the  items  are  54,  52J,  51£,  57,  50i,  54f,  51J, 
56J,  58  inches.  We  may  group  them  thus: 

(1)               (2)  (3) 

(50,  50i  51,  5U,  52,  52£, 

'   j    50i50f  51J,  51f  524,521 

Group  limits,  inches 50-50|  51-51f  52-52| 

Mean  of  group 50f              51f  52| 

and  so  on 

With  measurements  of  quarters  it  is  not  possible  to  de- 
vise a  grouping  such  that  the  mean  of  each  group  is  an 
even  number.  Neither  50J-51J  nor  50y-51  J  would  give  51 
as  the  mean. 

If,  however,  we  had  observations  in  which  the  fractions 
were  thirds,  or  fifths,  or  with  some  other  odd-numbered 
denominator,  we  might  do  so.  Thus  if  we  had  50f-51£  the 
mean  would  be  51;  or  if  we  had  50f-51£  the  mean  would 
be  51.  Sometimes  it  is  an  advantage  to  arrange  the  group 
so  that  the  mean  of  the  group  is  a  whole  number,  but  often 
this  does  not  matter. 

Again  let  us  suppose  we  are  dealing  with  whole  numbers 
and  decimals  (to  tenths  only).  Here  the  denominator  is  not 
an  odd  number.  We  might  arrange  the  groups  thus: 


GROUP  DESIGNATIONS  45 

(1)         (2)  (3)  (4) 

Limits 0      0.1-1.0     1.1-2.0    2.1-3.0    etc. 

Mean  of  group 0         0.55  1.55          2.55 

or 

(1)  (2)  (3) 

Limits 0-0.9  1.0-1.9  2.0-2.9 

Mean  of  group 0.45  1.45  2.45 

If  the  observations  were  made  to  the  nearest  hundredth 
we  might  have 

(1)  (2)  (3)  (4) 

Limits 0      0.01-1.00     1.01-2.00    2.01-3.00  etc. 

Mean 0       0.505  1.505  2.505 

« 

If  we  had  observations  of  much  greater  accuracy  we  would 
approach  the  following  round  numbers  as  the  means  of  the 
groups : 

(1)  (2)  (3)  (4) 

Limits..       0      0.  +  ...1.0         1. +  ...2.0        2.  +  .  .  .  3.0 
Mean...      0  0.5  1.5  2.5 

Group  designations.  —  In  describing  groups  it  is  techni- 
cally proper  to  designate  the  upper  and  lower  limits  of  the 
group.  For  whole  numbers  this  is  perfectly  simple.  Thus 
in  our  table  we  may  give 


(1)  0-4 

(2)  5-9 

(3)  10-14 

(4)  15-19  etc. 

If  the  whole  numbers  are  followed  by  fractions  we  may 
assume  that  any  fractions  are  attached  to  the  whole  num- 
bers and  that  the  maximum  figure  includes  the  largest 
possible  fraction  less  than  one.  Thus  19J  would  go  in  the 
fourth  group,  14.641  would  go  in  the  third  group.  The 
sign  (-)  here  stands  for  "  to,"  i.e.,  0  to  4. 


46  STATISTICAL  ARITHMETIC 

Sometimes  to  save  space  in  printing  only  one  group  limit 
is  given,  the  other  being  understood.  Thus  in  the  report 
of  the  Registrar  General  of  England  we  find  the  following 
age  groups  tabulated: 

Age 

0-  Meaning  0  to  4  plus  fractions 

5-  Meaning  5  to  9  plus  fractions 

10-  etc. 

15- 

Where  the  groups  differ  by  one,  this  method  is  the  only 
practicable  one.  Thus 

Age 
0- 
1- 
2- 
3- 

Here  we  could  not  state  an  upper  limit  without  using 
fractions. 

A  better  nomenclature  perhaps  would  be  to  use  the  plus 
sign  instead  of  the  dash,  indicating  that  any  fractions  were 
attached  to  the  whole  number.  Thus: 


0+ 
1+ 
2+ 
3+ 
etc. 

Let  us  compare  two  groupings,  a  and  6,  the  limits  of 
which  are  stated  as  follows: 


4+  4-4f 

5+  5-5| 

6+  6-61 


PERCENTAGE  GROUPING 


47 


The  inference  would  be  that  the  first  group  of  a  included 
items  of  magnitude  4  and  of  4  plus  any  fraction  attached 
to  it  however  smalt.  The  average  of  the  items  in  this 
group  would  be  4.5.  In  the  case  of  6,  however,  the  infer- 
ence would  be  that  the  measurements  were  made  to  the 
nearest  J,  and  that  the  items  in  the  first  group  would  be 
only  4,  4J,  4J  or  4f,  the  average  of  which  would  be  4f. 

Percentage  grouping.  —  It  often  happens  that  what  is 
wanted  is  not  so  much  the  number  of  items  which  fall  in 
each  group  as  the  relative  number  in  the  different  groups. 
In  this  case  we  take  the  total  number  of  items  as  100  per 
cent  and  find  the  per  cent  which  the  number  of  items  in 
each  group  is  of  the  total,  that  is,  we  make  a  percentage 
grouping,  or  a  percentage  distribution. 

In  a  certain  outbreak  of  typhoid  fever  the  cases  were 
distributed  according  to  age  as  follows: 


TABLE  10 

AGE  DISTRIBUTION  OF  TYPHOID 
FEVER  CASES 


Age  group. 

Number  of 
cases  in  group. 

Per  cent  of 
cases  in  group. 

(1) 

(2) 

(3) 

0-4 

42 

8.3 

5-9 

77 

15.3 

10-14 

82 

16.3 

15-24 

140 

27.7 

25-34 

85 

16.8 

35^4 

45 

8.9 

45- 

34     • 

6.7 

Total 

505 

100.0 

The  figures  in  the  third  column  are  computed  from  those 
in  the  second.  The  use  of  the  slide-rule  greatly  facilitates 
such  computations.  The  author  made  the  above  compu- 


48 


STATISTICAL  ARITHMETIC 


tation  of  percentages  with  the  slide-rule  in  less  than  two 
minutes.  For  comparison  he  made  the  same  computations 
by  long  division,  finding  that  it  required  three  times  as 
long. 

Cumulative  grouping.  —  A  cumulative  or  summation 
group  is  one  which  includes  the  data  for  previous  groups, 
that  is,  all  of  the  data  from  the  beginning  of  the  series  up  to 
the  group  limit.  An  illustration  will  make  this  clear. 

TABLE  11 

AGE  DISTRIBUTION   OF   CASES  OF  POLIOMYELITIS 
Brooklyn,  N.  Y.,  1916 


Age  group. 

Per  cent  of 
cases  in  group. 

Age  group 
(cumulative). 

Per  cent  in 
group. 

Age. 

Per  cent  less 
than  stated  age. 

(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

0- 

8.5 

0- 

8.5 

1 

8.5 

1- 

22.0 

0-1 

30.5 

2 

30.5 

2- 

23.9 

0-2 

54.4 

3 

54.4 

3- 

19.0 

0-3 

73.4 

4 

73.4 

4- 

7.2 

0-4 

80.6 

5 

80.6 

5- 

6.6 

0-5 

87.  2 

6 

87.2 

6- 

3.7 

0-6 

90.9 

7 

90  9 

7- 

2.5 

0-7 

93.4 

8 

93.4 

8- 

1.5 

0-8 

94.9 

9 

9^.9 

9- 

1.3 

0-9 

96.2 

10 

96.2 

10- 

0.8 

0-10 

97.0 

11 

97.0 

11-15 

2.0 

0-15 

99.0 

16 

99.0 

16- 

1.0 

0- 

100.0 

100.0 

100.0 

The  figures  in  the  fourth  column  were  obtained  by  suc- 
cessive additions  of  the  figures  in  the  second  column.  It  is 
more  common  perhaps  to  state  the  results  of  cumulative 
grouping  in  the  manner  shown  in  columns  five  and  six. 
If  there  are  30.5  per  cent  in  the  cumulative  group  0-1,  it  is 
obvious  that  30.5  per  cent  of  the  cases  were  younger  than 
2  years. 


AVERAGES  49 

The  summation  table  is  very  useful  in  many  statistical 
problems. 

Averages.  —  The  simplest,  most  common,  and  in  general 
the  most  useful  method  of  generalizing  the  results  of  a  set 
of  observations  is  the  average,  or  arithmetic  mean.  The 
word  mean  is  practically  synonymous  with  the  word  average, 
but  some  writers  apply  the  former  to  the  generalization  of 
a  group,  using  the  latter  to  indicate  the  arithmetical  process. 

The  average  is  found  by  dividing  the  sum  of  the  magni- 
tudes of  a  number  of  items  by  the  number  of  items.  The 

1  Q   _l_   1  Q  _l_  O'l          ^7 

average  of  13,  19  and  25  is  -  -  =  ^-  =  19.     The 

o  o 

12  +  14  +  10  +  5  +  9      50 

average  of  12, 14,  10, 5  and  9  is  -  -L-=—        - —  =  -r- 

o  o 

=  10. 

Now  what  is  the  average  of  all  the  items  in  both  of  these 

groups?    Without  thinking  we  might  say  that  it  is  - 

a 

—  14. |,  but  this  would  be  wrong.  To  prove  it  add  together 
the  items  and  we  have 

13  +  19  +  25  +  12  +  14  +  10  +  5  +  9  _  107  _        ' 
~~8~~  ~8~~ 

which  is  the  true  answer.  The  reason  why  we  cannot  take 
the  average  of  the  two  averages  is  because  the  second 
group  has  five  items  and  the  first  group  only  three.  The 
second  group  being  larger  ought  to  be  given  a  greater 
weight  in  combining  the  two. 

Suppose  that  we  give  the  second  group  greater  weight 
than  the  first  in  proportion  to  the  relative  numbers  of  items 
in  the  two  groups.  We  then  have 

19  (the  average  of  the  first  group)     X  3  =  57 

10  (the  average  of  the  second  group)  X_5  =  50 

The  sum  is  107 
and  107  -J-  8  =  13|. 


50 


STATISTICAL  ARITHMETIC 


This  is  what  is  called  a  "  weighted  average."  It  is  often 
very  useful.  Let  us  take  another  example  of  this. 

If  one  man  in  a  factory  earned  $30  per  week,  three 
earned  $20  and  one  hundred  earned  $10,  what  is  the  average 

wage  per  man?     Certainly  not  -  —     It  is 

o 

$30  X      1  =$     30 

$20  X      3  =       60 

$10  X  100  =    1000 

104    $)1090 

$10.48 

In  reality  this  is  merely  an  abridgment  of  the  labor  re- 
quired to  add  together  the  wages  of  each  particular  workman. 

Sometimes  it  is  required  to  find  the  average  of  a  series  of 
observations  arranged  by  groups.  Let  us  assume  that  in 
the  following  table  the  observations  are  made  only  to  the 
first  decimal  place. 

TABLE  12 


Group. 

Number  in  group. 

Average  of  group. 

Product  of  (2)  and  (3). 

(1) 

(2)    . 

(3) 

0-0.9 
1.0-1.9 
2.0-2.9 
3.0-3.9 

21 
17 

12 

8 

0.45 
1.45 
2.45 
3.45 

9.45 
24.25 
29.40 
27.60 

58 

58)90.70 
1.56  = 
average 

The  geometric  mean  of  two  numbers  is  the  square  root  of 
their  product.  If  we  have  two  numbers  a  and  b,  the  geo- 
metric mean  is  Vab.  It  is  also  called  the  mean  proportional 
between  two  numbers,  because  if  we  let  it  be  represented  by 
x,  then  a  :  x  =  x  :  b,  i.e.}  a  is  to  x  as  x  is  to  b.  By  al- 
gebra, from  this  equation  ab  =  x2.  .'.  x  =  Vab. 


AVERAGES 


51 


52 


STATISTICAL  ARITHMETIC 


If  there  are  three  numbers  the  geometric  mean  would  be 
the  cube  root  of  the  product  of  the  three  numbers;  and  so 
for  larger  numbers. 

As  compared  with  the  arithmetic  mean  the  geometric 
mean  minimizes  the  effect  of  very  large  numbers  and 
increases  the  effect  of  very  small  numbers  on  the  final  re- 
sults. For  instance,  the  arithmetic 
4+J20  24 
!  ~  2 


mean  of  4  and  20  is 


=  12.  The  geometric  mean  would 
be  V4X20  =  V80  =  8.95.  The 
arithmetic  mean  of  2]  and  100 
would  be  51,  the  geometric  mean 
14.1. 

Economists  often  use  the  geo- 
metric mean  in  combining  the 
prices  of  different  commodities 
to  obtain  an  index  of  trade  con- 
ditions. It  has  not  been  much 
used  in  demography,  but  there 
are  places  where  it  might  well  be 
used. 

There  is  another  kind  of  average 
known  as  the  harmonic  mean.  A 
man  travels  two  miles,  the  first  at  a 
rate  of  10  miles  per  hour,  the  sec- 
ond at  a  rate  of  20  miles  per  hour, 
what  was  his  average  rate  of  travel?  The  obvious  answer, 
i.e.,  15  miles  per  hour,  is  not  correct,  for  the  man  did  not 
travel  for  two  hours  but  for  two  miles.  Actually  he 
traveled  the  first  mile  in  ^  of  an  hour,  or  6  minutes,  and 
the  second  in  ^  of  an  hour,  or  3  minutes.  His  average 

/>          |          Q  f\ 

time,  therefore,  was  — ~ —  =  ~  =  4.5  minutes  per  mile,  and 


FIG.  6.  —  Machine  for 
Sorting  Cards. 


MECHANICAL  DEVICES  FOR  STATISTICAL  WORK      53 

60 

his  average  rate  j-=  =  13.3  miles  per  hour.  The  statis- 
tician seldom  has  occasion  to  use  this.  Algebraically  the 
harmonic  mean  of  two  numbers,  a  and  6,  is  ,  • 

In  the  study  of  data  arranged  in  series,  the  items  of  which 
fluctuate  up  and  down  but  which  nevertheless  show  cyclical 
variations,  the  moving  average  is  often  computed  in  order  to 
obtain  a  series  from  which  the  local  fluctuations  have  dis- 
appeared. The  moving  average  is  a  series  of  averages,  each 
based  on  the  same  number  of  items,  but  each  group  of  items, 
as  it  advances,  adding  one  new  item  and  dropping  one  old 
one.  If  for  example  we  have  items  in  this  order:  — 16,  14, 
18,  17,  18,  17,  19,  15,  13,  14,  11,  12,  10,  11,  8,  the  moving 
average  based  on  successive  groups  of  three  items  would  be 
16+14  +  18  _  14  +  18  +  17  lftQ  18+17+18 
"3"  "3~  =16'3;  ~3~ 

17.7)    :  -  =  17.3;  and  so  on.     Sometimes  groups 

of  five  items  are  taken,  or  nine,  or  twenty-one,  but  usually 
some  odd  number.  An  example  of  the  moving  average  may 
be  seen  in  Fig.  44.  Some  one  has  said  that  the  moving 
average  is  so  named  because  the  large  amount  of  work  re- 
quired moves  one  to  tears.  Any  one  thus  affected  should 
know  that  there  are  shortcuts  to  the  results  which  may  be 
found  described  in  works  on  general  statistics.  The  moving 
median  might  be  used  if  the  groups  chosen  contained  many 
items.  This  would  require  somewhat  less  work  than  the 
moving  average. 

Mechanical  devices  for  statistical  work.  —  It  would  not 
do  to  close  this  chapter  on  statistical  arithmetic  without 
calling  attention  to  the  mechanical  devices  now  available 
for  performing  the  operations  of  addition,  subtraction,  mul- 
tiplication and  division.  Where  statistical  operations  are 


54  STATISTICAL  ARITHMETIC 

constantly  going  on  these  instruments  more  than  pay  for 
their  cost.  They  are  too  well  known  to  need  description  here. 
The  tabulating  devices  of  the  Hollerith  and  Powers 
types  are  not  as  well  known,  but  they  have  become  an 
established  feature  in  the  U.  S.  Bureau  of  the  Census  and 
in  the  statistical  departments  of  large  commercial  and 
industrial  corporations.  Three  separate  devices  are  re- 
quired for  this  work  —  a  card  punching  machine,  a  sort- 
ing machine  and  a  counting  machine.  In  keeping  records 


FIG.  7.  —  Machine  for  Sorting  Cards. 

of  deaths,  the  data  from  each  death  certificate  are  trans- 
ferred to  a  card,  each  fact  being  indicated  by  number,  a 
hole  being  punched  in  the  proper  column.  These  holes 
serve  as  the  basis  of  sorting  in  the  second  machine.  By 
feeding  the  cards  into  the  sorting  machine  they  can  be 
quickly  divided  into  piles  according  to  age,  or  sex,  or  cause 
of  death,  or  into  other  groups  or  classes.  The  third  ma- 
chine counts  the  cards.1 

1  Information  concerning  these  devices  may  be  obtained  from  the 
Tabulating  Machine  Co.,  Ill  Devonshire  St.,  Boston,  Mass.  The 
author  is  indebted  to  this  company  for  figures  5,  6  and  7. 


HARVARD  UNIVERSITY-  DEMOGRAPHY 

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56  STATISTICAL  ARITHMETIC 


EXERCISES  AND   QUESTIONS 

1.  Define  the  following  statistical  units  as  used  by  the  U.  S.  Bureau 
of  the  Census. 

a.  A  family.  j.  A  rural  community. 

b.  A  birth.  k.  The  population  of  a  place. 

c.  A  death.  I.  Communicable  disease. 

d.  An  infant.  m.  Suicide. 

e.  A  dwelling  house.  n.  Age. 

/.  A  colored  person.  o.  A  citizen. 

g.  A  farmer.  p.  An  industrial  accident. 

h.  A  cotton-mill  operative.  q.  A  sleeping  room. 

i.  An  urban  community. 

2.  Criticize  the  tables  in  the  annual  reports  of  any  health  depart- 
ment (as  assigned  by  the  instructor),  as  to  title,  form,  boxing,  abbrevia- 
tions, etc. 

3.  Discuss  the  tables  in  the  reports  of  the  U.  S.  Bureau  of  the  Census. 
Should  they  be  taken  as  models? 

4.  Is  it  good  form  to  use  the  following  abbreviations? 

a.  "No.  of  Days,"  for  Number  of  Days. 

6.  "Pop."  for  population. 

c.  "  Av. "  for  average. 

d.  "Ty.  rate"  for  death-rate  from  typhoid  fever. 

e.  "T.  B.  rate"  for  death-rate  from  tuberculosis. 

What  other  ill-advised  abbreviations  have  you  observed? 

6.  In  one  ward  of  a  city  517  births  were  reported,  it  being  estimated, 
on  the  basis  of  past  experience,  that  this  figure  was  within  8  per  cent  of 
the  true  number;  in  a  second  ward  the  report  was  730  births,  with  an 
estimated  error  of  20  per  cent;  in  a  third  the  corresponding  figures  were 
910  and  25  per  cent;  in  a  fourth,  604  and  18  per  cent;  what  was  the 
probable  number  of  births  in  the  city?  And  what  was  the  probable 
percentage  error  of  the  total  number  of  reported  births? 

6.  If  the  death-rate  in  a  certain  city  was  20  per  thousand  in  1910, 
if  it  decreased  10  per  cent  the  next  year,  increased  10  per  cent  the  year 
after,  decreased  20  per  cent  the  next  year,  increased  20  per  cent  the  next 
year,  what  was  the' death-rate  in  1914? 


EXERCISES  AND  QUESTIONS  57 

7.  Multiply  the  following  numbers  by  the  arithmetic  process,  by  the 
use  of  logarithms  and  by  the  use  of  the  slide  rule.     Note  the  relative 
accuracies  of  the  result. 

a.  17  X  215.  /.  54,672  X  93,721. 

6.  95  X  847.  g.  4.7  X  1573. 

c.  2161  X  1050.  h.  0.231  X  1.29. 

d.  9230X40,373.  i.  0.507X0.062. 

e.  10,072  X  736.  j.  432.1  X  13.41. 

8.  Similarly  perform  the  following  divisions: 

a."  342  -e-  17.  /.  20,073  -^  98. 

6.  9467  +  872.  g.  763.05  H-  40.39. 

c.  473,561  -f-  2395.  h.  8999  -5-1101. 

d.  100,262  -=-  730.  i.  30,500  -r-  10.07. 

e.  0.517  -i-  2.43.  j.  0.03  -=-  76. 

9.  Given  the  following  items:  Find  the  mean,  the  median,  the  mode, 
the  upper  quartile. 

a.  6,  7,  6,  2,  8,  4,  9,  6,  7,  2,  1,  2,  1,  9,  8,  7,  3,  6,  6. 
6.  71,  3,  2,  0,  0,  1,  9,  5,  6,  3,  0,  2,  7,  7,  0,  4,  0,  2,  8. 
c.  2,  12,  2,  14,  3,  13,  9,  16,  1,  0,  40,  90,  3,  22,  7,  15. 

10.  Arrange  each  of  the  sets  of  figures  in  the  last  question  in  groups 
as  follows  and  find  the  average  of  each  set  from  these  groups. 

(1)          (2)  (3)  (4)  (5) 

Group  limits  (inclusive)       0-4      5-9     10-14     15-19     20  and  above 
Number  of  items  in  group 

11.  Find  the  arithmetic  and  geometric  means  of: 
a.  71  and  19.    b.   421  and  7.    c.   21,  7  and  11. 


CHAPTER  III 
STATISTICAL   GRAPHICS 

Use  of  graphic  methods.  — -  Statistics  are  numerical  ex- 
pressions of  facts.  When  the  facts  are  few  in  number  it  is 
not  necessary  to  use  figures  to  represent  them,  but  as  the 
number  of  facts  becomes  larger  a  point  is  reached  where 
memory  of  individual  facts  must  be  supplemented  by 
generalizing  them,  by  letting  a  number  stand  for  a  class  or 
a  group  of  facts.  In  the  same  way  when  the  numerical 
processes  become  complicated,  when  the  figures  become 
unwieldy  or  attain  magnitudes  beyond  the  ordinary  range 
of  familiarity,  it  is  useful  to  resort  to  another  process  and 
represent  the  figures  graphically.  And  even  when  the  facts 
are  few  and  simple  their  representation  by  ..diagram  is  often 
a  distinct  aid  to  the  mind  in  grasping  their  meaning  and 
fixing  them  in  the  memory. 

There  are  two  distinct  uses  of  graphic  methods  and  it  is 
important  to  keep  these  in  mind  in  preparing  diagrams. 
The  first  use  is  for  study.  The  relations  between  different 
groups,  classes  and  series  of  facts  can  often  be  understood 
better  from  diagrams  than  from  tables  of  figures.  By  the 
use  of  cross-section  paper  it  is  possible  to  interpolate  values 
between  plotted  points,  to  generalize  the  facts  of  a  series  in 
which  the  data  are  more  or  less  irregular,  to  extend  plotted 
curves  ahead  of  the  data,  thus  enabling  statistics  to  be  used 
as  a  basis  of  prediction,  to  compare  different  curves  and 
thus  establish  correlations.  Properly  used  graphic  methods 
will  greatly  assist  the  statistician  in  understanding  his  data. 

58 


TYPES  OF   DIAGRAMS  59 

It  is  a  great  mistake,  however,  to  think  that  all  statistics 
should  be  reduced  to  diagrammatic  form,  and  it  must  bo 
remembered  that  not  one  person  in  ten  is  able  to  read  a 
complicated  diagram  understandingly.  Some  regard  dia- 
grams as  puzzles  to  be  worked  out.  To  such  persons  dia- 
grams are  of  little  or  no  practical  value. 

The  other  use  of  graphic  methods  is  for  displaying  the 
facts  in  such  a  way  that  they  will  attract  attention,  that  the 
general  results,  regardless  of  details,  will  fix  themselves  in 
the  memory.  This  use  of  graphic  methods  has  greatly 
increased  in  recent  years.  We  see  diagrams  of  all  kinds  on 
bill-boards,  in  advertisements,  in  public  health  reports, 
in  popular  and  scientific  articles,  even  in  moving  pictures. 
The  growing  importance  of  the  whole  subject  is  shown 
by  the  recent  publication  of  a  notable  book  by  W.  C. 
Brinton1  on  Graphic  Methods  for  Presenting  Facts,  which 
contains  several  hundred  different  kinds  of  graphic  repre- 
sentations —  a  most  useful  book  for  statisticians  to  study. 

Thus,  on  the  one  hand,  we  have-  the  diagram  forming  a 
part  of  mathematics,  and,  on  the  other  hand,  we  find  it 
merging  into  the  cartoon;  hence  we  may  lay  down  the 
general  principle  that  graphic  methods  of  depicting  statis- 
tics must  be  selected  according  to  the  use  to  which  they  are 
to  be  put. 

Types  of  diagrams.  —  The  word  diagram  may  be  used  in 
a  generic  sense  to  include  all  of  the  various  kinds  of  mathe- 
matical graphs,  plots,  charts,  maps  and  pictorial  illus- 
trations used  by  statisticians  for  the  display  or  comparison 
of  numerical  data.  These  may  be  roughly  classified  as 
follows : 

1.  One-scale  diagrams,  in -which  different  items  are 
compared  with  each  other  on  the  basis  of  a  single 
magnitude  scale. 

1  See  list  of  references  in  Appendix. 


60  STATISTICAL  GRAPHICS 

2.  Two-scale    diagrams,    commonly   known   as   graphs, 

in  which  two  magnitudes  are  involved.  One  of 
these  is  commonly  represented  by  a  horizontal 
scale  and  one  by  a  vertical  scale.  These  graphs 
take  many  forms. 

3.  Three-scale   diagrams.     It   is   difficult   to   represent 

three  dimensions  on  a  flat  sheet  of  paper,  but  it  is 
sometimes  done  by  the  so-called  isometric  method. 

4.  Component-part  diagrams,  in  which  a  single  quantity 

is  shown  in  sub-division. 

5.  Pictorial  diagrams,  or  pictograms,  a  special  form  of 

the  one-scale  diagram  used  for  display. 

6.  Statistical  maps,  or  cartograms,  a  special  form  of  the 

two-scale  diagram,  in  which  one  scale  is  area  ar- 
ranged geographically,  while  the  other  consists  of 
differently  colored  or  shaded  areas. 

There  are  also  many  miscellaneous  types  of  diagrams 
with  specially  devised  irregular  scales,  logarithmic  scales, 
probability  scales,  etc.,  and  with  one  scale  superposed  on 
another.  These  are  for  study  and  not  for  display. 

The  appeal  to  the  eye.  —  Diagrams  are  intended  as  an 
appeal  to  the  eye,  and  advantage  is  taken  of  the  ability  of 
the  eye  to  observe  quickly  and  with  fair  accuracy: 

(a)  Distances,  as,  for  example,  the  relative  heights  of 

different  points  above  a  base  line  or  the  relative 
distances  of  points  from  some  other  point  or  from 
some  axis. 

(b)  Areas,  as  shown  by  comparison  of  similar  figures, 

that  is  by  circles,  squares,  rectangles  or  even 
irregular  figures. 

(c)  Volumes,  as  shown  by.  comparison  of  similar  cubes, 

cylinders,  spheres  and  irregular  figures. 

(d)  Ratios,  such  as  the  relative  lengths  of  parallel  lines, 

areas  or  volumes  similar  in  general  shape. 


GRAPHICAL  DECEPTIONS  61 

(e)    Slopes,  or  the  relative  inclinations  of  different  lines 
from  a  base  line. 

(/)    Angles,  as  shown  by  the  sub-division  of  the  360  de- 
grees about  a, point. 

(g)   Shades  and  colors,  as  shown  by  areas  on  pictograms 
and  maps. 

Graphical  deceptions.  —  In  preparing  diagrams  it  is  well 
to  bear  in  mind  that  the  eye  may  be  deceived.  There  may 
be  graphical  fallacies  as  well  as  statistical  fallacies.  Some 
of  these  may  be  illustrated  by  well-known  optical  illusions. 

In  Fig.  9  the  line  A  appears  to  be  longer  than  B.  In 
reality  they  have  the  same  length.  The  shaded  area  D  ap- 
pears to  be  taller  than  C.  In  reality  they  have  the  same 
height.  Astigmatism  is  also  the  cause  of  optical  illusions. 
Those  whose  business  it  is  to  prepare  diagrams  for  display 
should  study  these  optical  conditions. 

But  there  are  other  and  more  important  ways  in  which 
diagrams  may  deceive. 

In  pictograms  we  sometimes  see  two  objects  of  different 
size  —  say  two  men,  one  large  and  one  small,  illustrating 
the  relative  numbers  of  persons  who  have  died  from  two 
diseases.  If  the  relative  numbers  are  as  2  is  to  1,  the 
figures  would  naturally  be  drawn  with  the  heights  in  that 
ratio.  But  to  the  eye  the  larger  man  would  appear  to  be 
more  than  twice  the  size  of  the  smaller  one,  because  the 
eye  would  here  judge  not  the  height  alone,  but  the  whole 
aiea  of  the  figure  This  very  common  fallacy  in  which  one 
dimension  is  used  for  plotting,  with  no  reference  to  the 
other  dimensions  which  automatically  changes,  may  be 
illustrated  by  the  two  circles  E  and  F.  The  diameter  of 
F  is  only  twice  that  of  E,  but  the  circle  F  seems  to  be  much 
more  than  twice  as  large  as  E.  This  fallacy  may  be  called 
that  of  plotting  by  line  and  seeing  by  area. 

Similarly  when  a  polar  diagram  is  made  to  illustrate 


62 


STATISTICAL  GRAPHICS 


the  seasonal  distribution  of  some  disease,  the  number  of 
cases  per  1000  persons  being  indicated  by  the  distance  of 
each  plotted  point  from  the  center,  an  incorrect  idea  is 
obtained.  In  Fig.  21  the  death-rate  for  April  and  May 


FIG.  9.  —  Optical  Illusions. 

was  in  reality  only  three  times  that  for  August  and  Sep- 
tember, but  from  the  diagram  it  looks  to  be  more  than  three 
times  as  much.  The  reason  is  that  the  diagram  was  drawn 
as  a  line  diagram,  but  the  eye  sees  the  area  as  well  as  the 
lines  and  the  area  embraced  by  the  enveloping  lines  increases 
as  the  points  become  farther  from  the  center. 


ESSENTIAL  FEATURES  OF  A  DIAGRAM  63 

Other  fallacies  connected  with  the  choice  of  scales  will  be 
pointed  out  in  the  consideration  of  that  subject. 

Essential  features  of  a  diagram.  —  Every  diagram,  save 
the  very  simplest,  should  have  a  title;  one  or  more  scales, 
plainly  indicated;  a  background  of  cross-section,  or  co- 
ordinate lines;  the  points,  lines  or  areas  representing  the 
data  plotted,  marked  for  identification;  and  any  necessary 
notes  or  explanations.  As  a  rule  diagrams  should  be  self- 
contained,  that  is,  they  should  tell  the  facts  without  regard 
to  the  accompanying  text. 

The  title  may  be  entirely  outside  of  the  frame  of  coor- 
dinate lines,  with  the  idea  that  if  the  diagram  is  published 
the  printer  will  set  up  the  title  in  type.  This  simplifies 
somewhat  the  -construction  of  the  diagram,  but  if  a  lantern 
slide  is  made  it  may  be  that  the  printer's  type  will  be  found 
to  appear  disproportionately  small.  If  the  title  is  placed 
within  the  frame  of  coordinate  lines  these  lines  must  be  dis- 
continued and  not  allowed  to  run  through  the  letters  of  the 
title.  On  machine-ruled  paper  this  rule  cannot  hold  as  the 
coordinate  lines  cannot  be  erased.  It  is  possible  to  place  the 
title  on  a  piece  of  white  paper  and  paste  it  over  the  cross- 
section  lines.  In  the  case  of  machine-ruled  tracing  cloth, 
the  lines  may  be  removed  by  the  use  of  xylol,  or  gasolene, 
and  a  clear  background  obtained  for  the  title. 

In  designing  the  title  it  is  not  necessary  to  use  the  words 
"  Diagram  showing  the  .  .  .  "  any  more  than  it  is  necessary 
to  say  "  Table  showing  the  .  .  .  ." 

The  size  and  shape  of  the  diagram  will  depend  in  great 
measure  upon  the  scales  chosen,  but  as  diagrams  are  very 
often  reproduced,  even  though  not  drawn  primarily  for 
publication,  it  is  always  well  to  prepare  them  as  if  for 
publication. 

For  the  purposes  of  a  typewritten  report,  diagrams 
should  be  kept  within  the  limits  of  a  rectangle  7  by  9J  in. 


64  STATISTICAL  GRAPHICS 

The  standard  typewritten  paper  is  8J  X  11  in.,  but  there 
should  be  margins  of  1  in.  on  the  top  and  left  and  J  in.  on 
the  bottom  and  right  for  binding  and  trimming.  The 
paper  containing  the  diagram  should  be  cut  8J  by  11  in. 
Larger  diagrams  may  of  course  be  desirable  or  necessary. 

For  reproduction  most  diagrams  have  to  be  reduced 
in  size.  When  this  is  done  the  diagram  as  a  whole  is  not 
only  made  smaller  but  the  letters  are  made  smaller  and 
every  line  made  thinner.  Care  should  be  taken  therefore 
that  the  letters  and  figures  used  are  not  too  small  and  that 
the  lines  are  not  too  thin. 

As  a  rule  letters  and  figures  should  be  so  placed  that 
they  can  be  easily  read  from  the  bottom  or  the  right-hand 
edge. 

The  coordinate  lines  are  used  to  guide  the  eye  and  to 
enable  one  to  read  from  the  scale  with  accuracy  and  minute- 
ness. For  display  purposes,  however,  no  more  coordinate 
lines  should  be  used  than  are  necessary,  as  too  many  are 
confusing.  The  coordinate  lines  should  be  lighter  in  weight 
than  the  plotted  points  or  lines  in  order  that  the  latter  may 
stand  out  conspicuously. 

Too  many  plotted  lines  should  not  be  used  in  the  same 
diagram  as  confusion  may  result.  If  there  is  more  than 
one  plotted  line  each  should  be  clearly  marked.  This  is 
especially  important  if  the  lines  cross  or  meet  at  any  point: 

Often  it  is  desirable  to  have  the  diagram  include  within 
its  boundaries  not  only  the  graphic  representation  of  the 
figures,  but  the  figures  themselves. 

One-scale  diagrams.  —  The  simplest  diagram  is  one  where 
the  magnitudes  of  the  different  items  are  represented  by 
the  relative  lengths  of  lines  or  by  narrow  rectangles  of  con- 
stant width.  They  are  easy  to  understand  and  are  useful 
for  many  purposes.  The  magnitudes  represented  by  the 
lines  may  be  stated  in  figures  or  there  may  be  a  scale  shown 


ONE-SCALE  DIAGRAMS 


65 


for  comparison.     See  Figs.  10  and  11.     The  lines  may  be 
drawn  horizontally  or  vertically. 

An  important  principle  in  line  diagrams  is  that  all  of  the 
lines  should  start  from  the  same  base.  If  this  is  not  done 
comparison  is  difficult.  In  the  case  of  Fig.  11,  which  shows 
the  birth-rates  and  death-rates  for  two  European  countries, 


100- - 


1 

1 

"5 

i 

FIG.  10.  —  Numbers  Of  Deaths  from  Five  Most  Important  Causes. 
Cambridge,  Mass.,  1915. 

it  is  easy  to  compare  the  births,  shown  by  the  total  lengths, 
and  the  deaths,  shown  by  the  black,  because  they  start 
from  the  left-hand  line,  but  it  is  difficult  to  compare  the 
natural  increase  of  population  in  the  two  countries,  shown 
by  the  white,  because  they  have  no  common  base.  If  the 
natural  rate  of  increase  is  important  it  is  better  to  use  sepa- 
rate lines  for  births,  deaths  and  increase  as  shown  in  Fig.  11, 
b  and  c. 


66 


STATISTICAL  GRAPHICS 


It  is  also  difficult  to  compare  two  lines  which,  though 
they  have  a  common  base,  extend  in  opposite  directions 
from  the  base.  This,  however,  is  often  done  with  a  fair 
degree  of  satisfaction.  See  Fig.  42. 


10 


20 


30 


ENGLAND 

FIG.  11.  —  Comparison  of  Birth-rates,  Death-rates  and  Rates  of 
Natural  Increase. 

Diagrams  with  rectangular  coordinates.  —  Most  of  the 
diagrams  used  to  illustrate  statistics  are  of  the  two-scale 
type.  There  is  a  horizontal  scale  with  magnitudes  increas- 
ing from  left  to  right  and  a  vertical  scale  with  magnitudes 
increasing  from  bottom  to  top.  It  is  customary  also  to 
rule  in  a  sort  of  checker-board  consisting  of  parallel  ver- 
tical and  horizontal  lines  to  guide  the  eye  in  following  the 
scales  across  the  paper.  To  further  assist  the  eye  heavy 
lines  are  used  for  the  round  numbers  of  the  scale  and  finer 
lines  for  sub-divisions.  It  is  good  practice  also  to  always 
use  for  the  zero  line  a  line  as  heavy  as  the  plotted  line. 
Usually  this  would  be  the  bottom  line  and  the  left-hand 


DIAGRAMS  WITH  RECTANGULAR  COORDINATES     67 

line.  If  there  be  no  zero,  as  in  the  case  of  a  scale  of  years, 
the  heavy  line  would  not  be  used.  In  the  case  of  percent- 
age diagrams  both  the  zero  per  cent  line  and  the  hundred 
per  cent  line  should  be  heavy.  The  numerical  values  for 
the  sub-divisions  of  the  scale  are  shown  in  figures,  prefer- 
ably at  the  bottom  and  left  side  of  the  diagram.  Sometimes 
they  are  placed  also  at  the  top  and  right.  Thus  the  zeros  of 
both  scales  are  supposed  to  be  at  or  near  the  lower  left- 
hand  corner;  but  circumstances  may  compel  some  different 
arrangement. 

In  diagrams  of  this  kind  time,  whether  in  years,  months 
or  days,  is  generally  expressed  by  the  horizontal  scale 
and  always  runs  from  left  to  right.  Such  diagrams  are 
sometimes  called  historigrams,  sometimes  merely  graphs. 

The  distances  measured  along  the  vertical  scale  are  known 
to  mathematicians  as  ordinates,  the  distances  on  the  hori- 
zontal scale  as  abscissae. 

There  are  several  ways  of  plotting  with  two  scales. 
One  way  is  to  use  the  vertical  scale  as  a  measure  of  the 
length  of  certain  vertical  lines,  each  of  which  represents 
the  magnitude  of  an  item,  and  to  use  the  horizontal  scale  to 
indicate  the  occurrence  of  the  item.  Thus  in  Fig.  12  we 
have  a  daily  record  of  the  rainfall  for  one  month.  '  Each 
rainfall  is  represented  by  a  line  of  appropriate  length,  the 
position  of  the  line  showing  when  the  rain  occurred.  This 
method  is  especially  adapted  to  events  which  occur  intermit- 
tently, and  without  regular  gradations,  that  is  to  discrete 
series. 

The  rainfall  data  might  have  been  indicated  by  dots,  or 
crosses  placed  at  the  tops  of  the  lines,  the  latter  being  left 
out.  This  would  be  misleading,  however,  unless  similar 
dots  or  crosses  were  placed  on  the  zero  line  for  the  days  of  no 
rainfall.  This  would  not  look  well,  and  it  is  never  done. 

The  vertical  line  method  or  ordinate  plotting  is  sometimes 


68 


STATISTICAL  GRAPHICS 


used  for  plotting  data  in  series,  the  horizontal  scale  repre- 
senting time.  Thus  we  may  compare  the  death-rates  for 
different  years  by  a  diagram  such  as  that  shown  in  Fig.  13  A. 
This,  however,  is  a  continuous  series  and  may  be  plotted 


°.ru,y,.9i71£ 
FIG.  12.  —  Example  of  Plotting  a  Record  of  Rainfall. 


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FIG.  13.  —  Example  of  Simple  Plottings. 

as  a  broken  line,  known  as  a  profile  line,  which  shows 
continuity.  See  Fig.  13  B.  For  most  purposes  this  profile 
method  is  to  be  preferred  to  the  vertical  line  method,  but 
the  latter  is  perhaps  understood  better  by  persons  not 
familiar  with  graphic  methods. 


DSE  OF  THE  HORIZONTAL  SCALE 


Still  another  way  would  be  to  plot  the  data  as  dots,  or 
crosses,  and  draw  a  smooth  curve  through  them  to  show  the 
trend  of  events.  This  implies  that  the  data  are  subject 
to  errors  and  that  the  smooth  curve  gives  a  better  picture 
of  the  true  events.  See  Fig.  13  C.  The  art  of  smoothing 
curves  is  described  in  most  books  on  statistical  technique. 
In  general  it  may  be  said  that^the  rules  usually  laid  down 
are  based  on  the  laws  of  probability. 

Use  of  the  horizontal  scale.  —  In  the  illustrations  just 
given  the  divisions  of  the  horizontal  scale  were  taken  to  be 
definite  points  of  time,  namely  days  and  years,  each  point 
being  plotted  directly  on  a  vertical  line.  This  does  very 
well  for  plotting  yearly  records  which  run  on  continuously, 
and  there  is  no  objection  to  the  method  for  practical  pur- 
poses. It  is  not,  however,  strictly  accurate,  for  a  year  is 
not  a  point  of  time,  but  an  interval  of  time.  It  is  the  space 
between  the  lines,  which  represents  the  year,  the  vertical 
lines  marking  the  boundaries.  Graphs  are  sometimes  made 
on  this  basis. 

Let  us  plot  the  following  numbers  of  deaths  which  oc- 
curred in  the  different  months  of  a  single  year. 

TABLE  13 
NUMBER  OF  DEATHS:   EXAMPLE  FOR  PLOTTING 


Month. 

Death3. 

Month. 

Deaths. 

Month. 

Deaths. 

Month. 

Deaths. 

(1) 

(2) 

(1) 

(2) 

(1) 

(2) 

(1) 

(2) 

Jan. 

40 

Apr. 

27 

July 

20 

Oct. 

17 

Feb. 

30 

May 

23 

Aug. 

17 

Nov. 

20 

Mar. 

25 

June 

25 

Sept, 

15 

Dec. 

25 

Here  the  problem  is  to  divide  the  horizontal  scale,  which 
represents  a  year,  into  twelve  parts,  each  of  which  represents 
a  month,  and  plot  one  point  for  each  month.  Now  we  get 


70 


STATISTICAL  GRAPHICS 


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FIG.  14.  —  Examples  of  Time  Plotting. 

into  trouble  if  we  plot  the  data  on  the  lines,  for  we  might  do 
this  in  two  ways,  as  in  Fig.  14,  A  and  B.  In  one  case  we 
plot  the  point  at  the  beginning  of  the  month,  in  the  other, 
at  the  end  of  the  month.  Of  the  two  the  latter  is  to  be 
preferred.  It  would  be  more  logical  to  let  each  month  be 
represented  by  the  space  between  the  lines  and  to  plot 
the  points  in. the  middle  of  the  spaces  as  in  Fig.  14,  C  or  D. 
If  the  figures  plotted  represent  the  monthly  averages  of 


PLOTTING  FIGURES  BY  GROUPS 


71 


several  items  occurring  in  each  month  the  method  of  plot- 
ting shown  in  Fig.  14  E  is  a  proper  one.  Fig.  14  F  shows 
how  one  may  plot  the  mean  as  well  as  the  maximum  and 
minimum  item  for  each  month.  At  present  there  is  no 
well-established  custom  in  regard  to  these  methods.  Plot- 
ting 'on  the  line  is  usually  followed  simply  because  it  is 
easier  and  makes  a  neater  diagram.  Its  illogical  character 
seldom  causes  serious  misunderstandings. 

Plotting  figures  by  groups.  —  The  plotting  of  individual 
observations  is  comparatively  easy;  but  it  is  difficult  to 
decide  how  to  plot  the  totals  and  means  of  groups,  and  still 
more  difficult  if  the  groups  are  irregular.  This  can  best  be 
appreciated  by  an  example.  Let  us  undertake  to  plot  the 
following  data: 

TABLE  14 
DATA  TO  BE  PLOTTED 


Age 

(last  birthday). 

Number  of 
cases. 

Age  group. 

Number  of 
cases  in 
group. 

Average  number 
of  cases  for  each 
year. 

(1) 

(2) 

(3)    - 

(4) 

(5) 

0 

1 

1 

2 

2 

2 

0-4 

12 

2.4 

3 

4 

4 

3 

5 

1 

6 

4 

7 

3 

5-9 

15 

3.0 

8 

5 

9 

2 

10 

6 

« 

11 

4 

12 

7 

10-14 

25 

5.0 

13 

5 

14 

3 

15 

4 

16 

6 

17 

5 

15-19 

20 

4.0 

18 

3 

19 

2 

72 


STATISTICAL  GRAPHICS 


If  we  plot  the  individual  items  we  have  the  result  shown 
in  Fig.  15  A.  If  we  plot  the  total  numbers  of  cases  in 
each  group  we  may  do  so  by  the  methods  B,  C,  or  D. 
In  these  the  horizontal  scale  represents  not  individual  ages, 
but  groups.  We  may  indicate  this  fact  by  using  the 
hyphens  as  shown.  In  B  we  have  plotted  the  figure  12  on 
the  line  which  indicates  the  maximum  limit  of  the  group 
0-4,  15  on  the  line  which  indicates  the  maximum  limit  of 
group  5-9,  etc.  In  C  we  have  plotted  12,  15,  etc.,  in  the 
midcfle  of  the  spaces  which  represent  the  groups.  In  D 
the  height  of  the  horizontal  line  above  the  base  is  taken 
to  represent  the  total  and  extends  across  the  group  limits. 
If  we  wish  to  show  both  the  individual  observations  and 
the  means  for  the  groups  we  may  plot  as  in  E. 

In  plotting  by  groups  care  should  be  taken  to  make  it 
clear  that  the  horizontal  scale  stands  for  groups  and  that 
the  vertical  scale  stands  for  the  number  in  the  group. 

Plotting  irregular  groups.  —  Let  us  now  take  the  case 
of  irregular  groupings.  Assume  the  following  data: 


TABLE  15 
DATA  TO  BE  PLOTTED 


Age  group. 

Number  of 
cases  in  group. 

Average  for 
eacb  year  in 
group. 

(1) 

(2) 

(3) 

0-  4 

4 

0.8 

5-  9 

6 

1.2 

10-14 

8 

1.6 

15-19 

6 

1.2 

20-29 

7 

0.7 

30-39 

5 

.     0.5 

40-59 

8 

0.4 

60-79 

6 

0.3 

80-99 

3 

0.15 

PLOTTING  IRREGULAR  GROUPS 


73 


5 10 15 20 

Age  Group 


5 10- 

Age  Group 


30 


10 


5  10  15  20 

Age  Group 

FIG.  15.  —  Examples  of  Age  Plotting. 


74 


STATISTICAL  GRAPHICS 


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SUMMATION  DIAGRAMS  75 

In  the  first  place  we  must  find  some  way  to  indicate  to 
the  eye  the  varying  intervals  of  the  group.  The  first  four 
groups  cover  five  years,  the  next  two  ten  years  and  the 
last  three  twenty  years  each.  We  might  do  this  as  in 
Fig.  16  A,  in  which  the  heavy  vertical  lines  indicate  the 
group  limits..  In  B  the  coordinate  lines  are  regular  and  the 
group  limits  are  shown  by  the  emphasized  horizontal  scale. 
In  C  the  blocks  indicate  the  group  limits.  Not  one  of  these, 
however,  gives  an  adequate  picture  of  the  distribution  of 
the "  cases  according  to  age,  because  the  groups  are  not 
uniform.  All  three  diagrams  are  fallacious  because  the 
ordinates  are  not  strictly  comparable.  The  best  way  to 
show  distribution  by  age  is  to  make  the  groups  comparable 
by  reducing  all  to  a  common  denominator.  This  can  be 
done  by  finding  the  average  number  of  cases  for  each  year 
in  the  group.  The  results  are  shown  in  Fig.  16  D.  Here 
the  irregular  grouping  on  the  horizontal  scale  is  maintained, 
yet  a  good  idea  is  given  of  the  distribution  of  the  cases 
according  to  age. 

Summation  diagrams.  —  For  many  purposes  it  is  desir- 
able to  plot  the  results  obtained  by  the  successive  summa- 
tion of  the  items  in  preceding  groups.  This  gives  what  are 
called  summation  diagrams,  cumulative  plots,  mass  plots  or 
mass  curves.  This  may  be  illustrated  by  the  data  on  p.  77. 

These  data  are  plotted  in  Fig.  17.  Sometimes  instead 
of  connecting  the  plotted  points  by  straight  lines  a  curved 
line  passing  approximately  through  them  is  sketched  in. 
It  should  be  noticed  that  in  this  diagram  the  horizontal 
scale  stands  for  age  and  not  for  age-groups. 

One  use  which  can  be  made  of  a  plot  of  this  kind  is  to 
find  the  median  of  the  series.  There  are  53  cases  in  all. 
The  middle  one  is  the  27th.  From  the  scale  this  item  has  a 
value  of  24  years,  as  shown  by  the  cross.  In  the  same  way 
the  quar tiles  may  be  found  and  the  decentiles. 


76 


STATISTICAL  GRAPHICS 


i 


/ 


10          CO          30          40          50          60          TO          80          90  ,      100 

Age 

j.  17.  —  Example  of  Cumulative,  or  Summation  Plotting. 


CHOICE  OF  SCALES 


77 


TABLE   16 
DATA  TO  BE  PLOTTED 


Age-group. 

Number  of 
cases. 

Summation  group. 

Number  of 
cases. 

Less  than  age. 

(1) 

(2) 

(3) 

f4) 

(5) 

(M 

4 

(M 

4 

5 

5^9 

6 

0-9 

10 

10 

10-14 

8 

0-14 

18 

15 

15-19 

6 

0-19 

24 

20 

20-29 

7 

0-29 

31 

30 

30-39 

5 

0-39 

36 

40 

40-59 

8 

0-59 

44 

60 

60-79 

6 

0-79 

50 

80 

80-99 

3 

0-99 

53 

100 

Total 

53 

53 

Another  use  is  that  of  redistributing  the  cases  according 
to  a  different  age-grouping.  Let  us  suppose  that  we  desire 
to  find  the  number  of  cases  between  the  ages  of  35  and  45, 
i.e.,  in  age-group  35-44.  From  the  vertical  scale  and  the 
plotted  curve  we  find  that  there  are  38  cases  below  age  45 
and  33  cases  (approximately)  below  age  35,  hence  there 
are  38  —  33  =  5  cases  in  age-group  35-44.  This  principle 
may  be  usefully  applied  in  redistributing  the  population  of 
a  city  into  age-groups  in  connection  with  the  computation 
of  specific  death-rates. 

Choice  of  scales.  —  The  choice  of  both  scales  is  a  matter 
of  great  importance,  for  it  not  only  influences  the  size  and 
shape  of  the  diagram,  but  controls  the  slopes  of  plotted  lines 
and  the  apparent  differences  between  plotted  points.  In 
Fig.  18  we  have  the  death-rates  of  Moscow  from  1881  to 
1910  plotted  by  five-year  groups  according  to  two  dif- 
ferent scales.  The  two  diagrams  look  to  be  quite  different, 
and  B  gives  the  impression  of  a  greater  decrease  in  rate 


78 


STATISTICAL  GRAPHICS 


10 


than  A  because  on  account  of  the  greater  vertical  scale 

and  the  smaller  horizontal  scale  the  slope  of  the  plotted 

line  is  more. 

Sometimes   for  purposes   of   comparison   two   lines  are 

plotted  on  the  same  sheet,  each  having  its  own  vertical 

scale.  Here  the  choice  of 
the  proper  scale  is  all-im- 
portant. 

It  sometimes  happens 
that  in  order  to  show  the 
desired  variations  in  a  series 
of  plotted  ordinates  a  scale 
must  be  chosen  so  large 
that  the  zero  point  would 
fall  too  far  below  the 
plotted  point  to  have  it  ap- 
pear on  the  diagram.  Right 
here  lurks  a  graphical  fallacy 
which  may  be  serious.  It  is 
best  appreciated  by  study- 
ing an  actual  illustration. 
Fig.  19  shows  the  general 


35 


25 

I80 
I15 

10 


death-rate   and   the    tuber- 
culosis death-rate  per  1000 
SSSSS33  inhabitants    in   Boston, 

FIG.   18.  —  Death-rates:    Moscow,   Massachusetts,    from    1881 


Showing   Effect    of  to    ign     thfi    fi  bei 

Changing  Scales.  ,          ,    . 

plotted  in  five-year  groups. 

In  A  different  scales  are  used  and  the  scales  do  not  ex- 
tend to  zero  on  the  base  line.  In  R  the  same  scale  is 
used  for  both  series  of  items.  From  diagram  A  one  would 
get  the  idea  that  the  tuberculosis  rate  was  decreasing 
much  faster  than  the  general  death-rate,  but  from  diagram 
B  the  opposite  idea  would  be  obtained. 


CHOICE  OF  SCALES 


79 


20 


20 


15' 


10 


25 


15, 


10' 


FIG.  19.  —  Comparison  of  Deaths  from  Tuberculosis  with  Deaths 
from  all  Causes:  Boston,  Mass.  A,  Incorrect  Method.  B, 
Correct  Method. 


80 


STATISTICAL  GRAPHICS 


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C 

\ 

\ 

"\ 

w 

\ 

X 

FIG.  20.  —  Example  of  Not  Carrying  Scale  to  Base  Line.     Tuber- 
culosis Death-rate:    Boston,  Mass. 


DOUBLE  COORDINATE  PAPER  81 

Fig.  20  shows  the  reduction  of  the  tuberculosis  death- 
rate  in  Boston  expressed  in  terms  of  the  percentage  which 
the  death-rate  of  each  period  was  of  that  for  the  period  1881 
to  1885.  In  B  the  vertical  scale  is  carried  down  to  0  per 
cent  at  the  base  line.  This  gives  a  true  picture  of  the  re- 
duction which  has  taken  place  and  the  death-rate  remaining. 
In  A  the  vertical  scale  is  not  carried  to  the  base  line  and  the 
diagram  gives  the  optical  impression  that  the  reduction 
has  been  greater  than  it  actually  has  been  and  that  the  rate 
at  the  end  of  the  period  was  very  much  less  than  at  the 
beginning.  Brinton  has  suggested  that  when  the  base  line 
does  not  represent  the  zero  of  the  vertical  scale  it  should  be 
drawn  as  a  wavy  line  instead  of  a  straight  line,  and  this 
idea  has  much  merit.  Where  two  different  vertical  scales 
are  used,  and  one  goes  to  zero  at  the  base  line  while  the  other 
does  not,  the  wavy  line  may  extend  only  half  way  across 
the  diagram  from  that  side  of  the  diagram  where  the  scale 
does  not  go  to  zero.  C  in  Fig.  20  illustrates  the  appear- 
ance of  a  diagram  drawn  in  this  way.  The  wavy  line 
implies  that  the  lower  part  of  the  diagram  is  omitted. 

Diagrams  with  polar  coordinates.  —  Fig.  21  illustrates 
a  diagram  with  the  ordinates  represented  by  distances 
from  a  central  point  along  radial  lines,  the  abscissae,  if  we 
may  use  the  term  out  of  its  place,  being  represented  by  the 
angle  which  the  ordinate  makes  with  the  vertical  measured 
clockwise  around  the  circle.  This  form  of  plotting  has 
a  limited  application  and  because  of  its  inherent  fallacious 
character  should  be  abandoned. 

Double  coordinate  paper.  —  Sometimes  it  is  convenient 
to  use  what  may  be  called  double  coordinate  paper.  This 
is  illustrated  by  Fig.  22.  Here  the  plotted  line  may  be 
read  against  either  set  of  coordinates.  The  horizontal 
lines  give  the  number  of  deaths  from  typhoid  fever,  the 
scale  being  at  the  left.  The  inclined  lines  give  the  death- 


82 


STATISTICAL  GRAPHICS 


rate  per  100,000.  Thus  in  1900  the  number  of  deaths 
was  about  305,  the  death-rate  about  27  per  100,000.  The 
slope  of  the  inclined  lines  depends  upon  the  increase  in 
population.  The  black  inclined  line  represents  popula- 
tion and  this  may  be  read  for  the  censal  years  from  the 
right-hand  scale.  It  will  be  seen  that  the  ratio  between 


FIG.  21.  —  Example  of  Radial  Plotting. 

the  right-hand  and  left-hand  scale  for  any  horizontal  line 
gives  the  rate  for  the  heavy  line,  i.e.,  200  -f-  1,000,000  = 

20 
100  000'  °r  2°  per  hundred  thousand.     So  also  100  -4-  500,000 

=  20  per  hundred  thousand.  Any  point  on  the  heavy 
line,  therefore,  gives  a  rate  of  20  per  hundred  thousand. 
The  rate  line  for  10  per  100,000  is  one-half  way  to  the  line 
between  the  heavy  line  and  the  zero  or  base  line,  on  each 
vertical  line  which  represents  a  census.  The  rate  line  of  30 
is,  on  each  vertical,  as  far  above  the  black  line  as  the'rate 
line  of  10  is  below  it.  And  so  on. 

In  the  example  chosen  the  typhoid  fever  rate  in  Brooklyn 
has  fallen  since  the  date  of  the  last  plotting,  i.e.,  1906. 


RATIO  CROSS-SECTION  PAPER 


83 


€061 


0061 


068 1 


0881 


5Z8L 


ff3A3d  QIOHdAl  WOUd  SH1V3Q  dO 


Ratio  cross-section  paper.  —  Thus  far  we  have  been 
dealing  with  regular  scales  in  which  the  intervals  are  uni- 
form from  one  end  to  the  other.  It  is  possible  to  construct 
scales  with  intervals  which  are  not  uniform,  but  which  vary 
in  a  systematic  way.  These  are,  used  for  special  purposes. 
The  most  common  scale  of  this  kind  is  the  logarithmic  scale. 


84 


STATISTICAL  GRAPHICS 


Diagrams  in  which  the  vertical  scale  is  logarithmic  and  the 

horizontal    scale    uniform    are    sometimes    called    "  ratio 

charts."     These  have   been   used  by  engineers   for   many 

years,  but  they  are  only  beginning  to  be  appreciated  by 

statisticians. 

_It  will  be  recalled  that  the  logarithms  of  the  decimal 

numbers  are  as  follows: 

TABLE  17 
LOGARITHMS  OF  NUMBERS 


Number. 

Logarithm. 

(1) 

(2) 

1 

0.000 

10 

l.OOO- 

100 

2.  COO 

1,000 

3.000 

10,000 

4.000 

100,000 

5.000 

1,000,000 

6.000 

As  each  number  increases  tenfold  the  logarithm  increases 
by  one;  and  in  general  it  may  be  said  that  as  numbers 
increase  at  a  regular  rate  the  logarithms  increase  by  a 
regular  increment.  From  the  logarithm  tables l  it  may  be 
seen  that  the  log  of  10  is  1.0000,  and  that  if  10  is  increased 
by  25  per  cent  and  becomes  12.5  the  log  of  12.5  is  1.0969. 
an  increment  of  0.0969.  The  log  of  50  is  1.6990.  50  in- 
creased by  25  per  cent  is  62.5.  The  log  of  62.5  is  1.7959, 
an  increment  of  0.0969  as  before.  The  log  of  1570  is  3.1959. 
1570  increased  by  25  per  cent  is  1962.5  and  the  log  of  this 
is  3.2928,  an  increment  of  0.0969  as  before.  If,  using  a 
uniform  scale,  we  plot  figures  which  increase  at  a  constant 
rate  we  shall  get  a  curve  as  shown  in  Fig.  23  A.  Let  us 
1  See  Appendix. 


RATIO  CROSS-SECTION  PAPER 


85 


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248 
207 
173 
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120 
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Population  on 
Logarithmic  Scale 

§  g  i  §  i  Sis 

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FIG.  23.  —  Example  of  Logarithmic  Plotting. 


86 


STATISTICAL  GRAPHICS 


start  with  a  population  of  100  in  1870  and  assume  an  in- 
crease of  20  per  cent  each  decade.  We  then  have  the 
following : 

TABLE  18 
DATA  TO  BE  PLOTTED 


Year. 

Population. 

Log  of  popu- 
lation. 

(1) 

(2) 

(3) 

1870 

100 

2.0000 

1880- 

120 

2.0792 

1890 

144 

2.1584 

1900 

173 

2.2380 

1910 

207 

2.3160 

1920 

248 

2.3945 

1930 

299 

2.4757 

The  figures  in  column  (2)  are  plotted  in  A.  If  we  plot  the 
logarithms  of  the  numbers  in  column  (2)  we  have  a  straight 
line  as  in  B.  This  being  so,  why  not  label  the  horizontal 
lines  with  the  numbers  in  column  (2)  instead  of  their 
logarithms?  This  is  done  at  the  right  of  the  diagram.  It 
will  be  seen  that  the  vertical  scale  is  not  made  up  of  uni- 
form intervals,  but  aside  from  that  fact  it  is  a  perfectly 
good  scale.  In  C  we  have  a  diagram  in  which  the  vertical 
scale  (represented  by  the  horizontal  lines)  is  drawn  on  this 
basis,  and  it  will  be  seen  that  the  figures  in  column  (2) 
plotted  on  it  fall  in  a  straight  line.  This  is  a  single  loga- 
rithmic, or  in  simpler  words,  a  ratio  chart.  Figures  increas- 
ing at  a  constant  rate  plot  out  as  a  straight  line  on  paper 
thus  ruled,  i.e.,  with  a  uniform  horizontal  scale  and  a 
logarithmic  vertical  scale. 

There  are  two  uses  for  single  logarithmic  paper.  One  is 
to  show  variations  in  rate.  If  we  plot  the  population  of 
the  United  States  on  ordinary  cross-section  paper  with 


RULED  PAPER  87 

uniform  scales  we  obtain  an  ascending  curve,  but  from  this 
we  get  no  idea  of  the  constancy  of  the  rate  of  increase. 
This  is  shown  in  Fig.  24  A.  But  if  we  use  ratio  cross- 
section  paper,  as  in  B,  we  find  that  the  rate  of  increase 
was  constant  from"  1790  to  1860,  but  that  since  the  Civil 
War  the  rate  has  been  nearly  constant  yet  not  as  great  as 
before.  On  this  paper  equal  slopes  mean  equal  rates  of  in- 
crease, while  on  uniform  paper  equal  slopes  mean  equal  in- 
crements. 

Another  use  is  that  of  enabling  us  to  plot  on  one  sheet 
observations  which  cover  a  very  wide  range.  If  we  were 
using  a  uniform  scale  to  plot  such  figures  we  should  have  to 
make  the  scale  so  small  that  individual  differences  between 
the  small  numbers  could  not  be  discerned.  It  will  be 
noticed  that  on  the  ratio  paper  the  intervals  for  the  small 
numbers  are  larger  than  for  the  high  numbers,  so  that  if 
plotted  on  this  paper  we  can  still  read  differences  in  the 
lower  part  of  the  scale.  The  upper  part  of  the  scale  is 
foreshortened.  In  fact  we  can  discern  the  same  percent- 
age differences  in  all  parts  of  the  scale. 

Logarithmic  cross-section  paper.  —  By  logarithmic  cross- 
section  paper  we  usually  mean  paper  on  which  both  the 
horizontal  and  the  vertical  scales  are  logarithmic.  Here 
the  ratios  are  in  both  directions.  It  will  be  observed  that 
the  interval  from  1  to  10  is  the  same  as  that  from  10  to  100, 
from  100  to  1000  and  so  on.  One  objection  to  the  loga- 
rithmic scale  is  that  it  does  not  go  to  zero.  The  interval 
below  1  runs  from  1  to  0.1,  the  next  from  0.1  to  0.01,  the 
next  from  0.01  to  0.001  and  so  on. 

This  paper  is  very  largely  used  in  scientific  work,  but  its 
use  for  statistical  purposes  is  somewhat  limited. 

Ruled  paper.  —  It  is  not  difficult  to  rule  your  own  cross- 
section  paper,  although  it  is  tedious  work.  Many  sorts 
of  ruled  papers  are  on  the  market  and  can  be  purchased 


88 


STATISTICAL  GRAPHICS 


Direct  Scale 


Logarithmic  Scale 


I     1 


FIG.  24.  —  Population  of  the  United  States  shown  by  Direct  and 
Logarithmic  Plotting. 


MECHANICS  OF  DIAGRAM   MAKING  89 

from  dealers  in  engineering  drawing  materials.     The  fol- 
lowing scales  are  convenient  for  ordinary  work: 

(a)    Inches  subdivided  into  tenths  in  both  directions. 

(6)    Half  inches  subdivided  into  tenths  in  both  directions. 

(c)  Inches  subdivided  into  tenths  in  one  direction  and 

into  twelfths  in  the  other  direction,  — useful  for 
plotting  data  for  the  twelve  months  of  a  year. 

(d)  Ratio  paper,  with  inches  subdivided  into  tenths  in 

one  direction,  and  with  a  logarithmic  scale  from 
1  to  10,000  in  the  other  direction. 

(e)  Arithmetical  probability  paper. 
(/)    Logarithmic  probability  paper. 

(g)  Paper  with  horizontal  scale  ruled  for  the  calendar 
year,  and  vertical  scale  in  inches  subdivided  to 
tenths. 

It  is  possible  to  buy  tracing  cloth  ruled  in  cross-section 
form,  but  the  kinds  of  ruling  are  limited.  Such  cross- 
section  tracing  cloth  is  sold  by  the  yard,  width  about 
26  in.,  and  may  be  cut  to  sheets  of  desired  size. 

•  Mechanics  of  diagram  making,  —  For  making  diagrams 
it  is  advisable  to  provide  a  regular  draughtsman's  equip- 
ment. This  should  include: 

(a)  A  drawing  board  of  appropriate  size.  For  small 
diagrams  a  size  of  about  12  in.  by  17  in.  is  satis- 
factory. 

(6)  A  tee-square  long  enough  to  extend  across  the 
drawing  board. 

(c)  A  30-degree  triangle,  10  in.  long,  celluloid. 

(d)  A  45-degree  triangle,  6  in.  long,  celluloid. 

(e)  A  lettering  triangle,  to  give  slopes  for  letters. 
(/)    A  ruling  pen. 

(g)   One  or  more  scales,   steel,   celluloid    or    boxwood, 

variously  ruled  in  tenths,  quarters,  etc. 
(k)    Black  drawing  ink  (Higgins). 


90 


STATISTICAL  GRAPHICS 


Jan. 
F 


FIG.  25.  —  Examples  of  Plotting  Paper.     Sheets  8£  X  11  inches. 


LETTERING  91 

(i)    Thumb  tacks. 

(j)    Brown  "  detail "  paper. 

(k)   Tracing  cloth. 

Other  equipment  may  be  needed  according  to  the  nature 
of  the  work. 

Lettering.  —  There  is  much  truth  in  the  statement  that 
good  letterers  are  born  and  not  made.  Yet  it  is  surprising 
how  much  one  can  improve  in  lettering  by  giving  attention 
to  a  few  guiding  principles. 

For  most  diagrams  it  is  best  to  adopt  a  very  simple  style 
of  letter.  Shaded  letters  look  well  on  maps,  but  are  out  of 
place  on  line  diagrams.  The  two  styles  shown  in  Fig.  26 
are  suitable  for  ordinary  work.  The  choice  of  a  vertical 
letter  or  a  sloping  letter  is  largely  a  matter  of  taste.  Most 
people  are  more  successful  with  sloping  letters.  They  can 
be  made  a  little  more  rapidly,  but  they  are  perhaps  a  little 
more  informal  than  vertical  letters. 

It  is  important  that  letters  appear  to  be  uniform  in 
height  and  slope.  It  is  well  to  use  guides  both  as  to  height 
and  slope.  Letters  should  also  appear  to  be  spaced  uni- 
formly. The  curves  of  such  letters  as  C,  G,  O  and  S  should 
extend  slightly  above  and  below  the  horizontal  guide  lines. 
Adjacent  straight-line  letters  such  as  N,  I,  IT,  M,  etc., 
should  be  spaced  a  little  farther  apart  than  curved  letters. 
Attention  should  be  given  to  the  manner  of  making  the 
strokes  as  shown  in  the  plate. 

The  student  should  consult  a  book  on  lettering  such,  for 
example,  as  that  of  Reinhardt. 

If  the  title  is  inset  it  should  be  carefully  placed.  In 
general  the  lower  right-hand  corner  is  the  best  place  for  it, 
but  often  its  location  is  governed  by  available  space. 
The  sizes  of  letters  used  should  follow  the  important  words. 
Each  line  should  be  centered.  Write  each  line  on  a  scrap 
of  paper:  count  the  letters  in  it:  find  the  middle  letter: 


92 


STATISTICAL  GRAPHICS 


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put  that  down  first  and  then  letter  backwards  and  forwards. 
Capitals  may  be  used  for  the  principal  lines  of  a  title.  In 
a  general  sort  of  way  try  to  arrange  the  lines  so  that  a  line 
circumscribing  the  title  will  be  approximately  an  ellipse. 

Label  each  scale,  except  that  it  is  unnecessary  to  do  so 
in  the  case  of  months  and  years.     Do  not  use  abbreviations. 


THE  USE  OF  COLOR  IN  DIAGRAMS  93 

If  there  is  more  than  one  plotted  line  label  each  one.  Be 
free  in  the  use  of  explanatory  notes.  A  diagram  should 
tell  its  own  story.  In  doing  this  use  letters  of  readable  size. 
It  is  a  good  rule  never  to  make  a  letter  or  a  figure  less  than 
\  inch  in  height. 

Somewhere  on  the  sheet,  but  outside  of  the  diagram 
itself,  should  be  placed  the  initials  of  the  person  who  made 
the  diagram  and  the  date.  This  is  valuable  for  identifica- 
tion, but  it  need  not  be  published. 

Wall  charts.  —  Wall  charts  are  much  used  nowadays  in 
the  display  of  vital  statistics.  It  is  not  difficult  to  prepare 
these,  but  certain  general  principles  should  be  kept  in 
mind.  They  should  be  simple  and  clear,  of  ample  size 
and  plainly  lettered.  If  intended  to  be  seen  from  a  dis- 
tance the  letters  should  be  large  and  the  lines  heavy.  As 
lettering  forms  an  important  part  of  a  wall  diagram  it  is 
well  to  know  that  gummed  letters  of  all  sizes  can  be  pur- 
chased. Examples  of  these  letters  are  shown  in  Fig.  27. 

The  use  of  color  in  diagrams.  —  Colored  lines  should  be 
used  sparingly  if  the  diagrams  are  to  be  published.  A 
sheet  must  go  tlirough  the  press  once  for  each  color  and  this 
adds  to  the  cost.  The  most  effective  use  of  color  is  where 
a  single  colored  line  is  made  to  stand  out  in  contrast  to 
other  black  lines,  and  for  this  purpose  red  is  the  best. 
Color  on  plotted  lines  may  be  avoided  by  using  black  lines 
made  in  different  ways.  The  following  are  easily  dis- 
tinguishable : 


1.  Heavy  full  line 

2.  Light  full  line 

3.  Heavy  broken  line 

4.  Light  broken  line 

5.  Dotted  line 

6.  Dot-dash  line 


94  STATISTICAL  GRAPHICS 

For  wall  charts  or  posters  intended  to  be  viewed  from  a 
distance,  colors  are  justifiable. 

The  cross-section  lines  on  the  ruled  paper  ordinarily  sold 
are  colored  green  or  brown  or  light  red.  Very  bright  colors 

1234567890. 


BC 


FIG.  27.  — Examples  of  Gummed  Letters,  .Useful  for  Wall 
Diagrams. 

used  for  this  purpose  are  exceedingly  trying  on  the  eyes. 
It  is  desirable  however  to  have  a  color  which  can  be  pho- 
tographed and  also  blue-printed.  Green  is  not  satisfac- 
tory from  these  points  of  view.  Dull  red  is  much  better. 
Vermilion  red  should  be  used,  not  carmine. 


COMPONENT  PART  DIAGRAMS 


95 


Component  part  diagrams.  —  In  order  to  show  the  com- 
ponent parts  of  a  total  number  we  may  subdivide  a  line  or 
a  long  rectangle  and  label  each  part,  or  we  may  subdivide 
an  area,  as  a  square  or  a  circle,  indicating  differences  by 


FIG.  28.  —  Proportion  of  Deaths  from  Each  Specified  Cause  in 
the  U.  S.  Registration  Area:  1907. 

colors,  shades  or  patterns  as  in  cartography.  A  circle 
properly  subdivided  is  perhaps  the  best  type  of  diagram  to 
show  percentages.  Here  the  sectors  plainly  show  the  de- 
sired differences.  This  sort  of  a  diagram  is  not  to  be  con- 
fused with  plotting  by  polar  coordinates.  (See  Fig.  28.) 


96  STATISTICAL  GRAPHICS 

Statistical  maps.  —  The  object  of  statistical  maps  is  to 
display  classes  and  groups  of  statistics  for  different  areas. 
It  will  be  remembered  that  statistical  classes  involve  differ- 
ences which  cannot  be  expressed  in  figures,  but  that  statisti- 
cal groups  contain  facts  similar  in  kind  but  which  differ  from 
each  other  numerically.  This  difference  should  be  kept  in 
mind,  in  preparing  statistical  maps. 

The  statistical  data  are  shown  on  maps  by  different 
colors,  by  different  patterns  of  lines  and  dots  or  by  sur- 
face shadings.  In  the  display  of  data  arranged  in  groups, 
that  is,  in  accordance  with  magnitude,  it  is  well  to  indicate 
the  differences  by  variations  in  shade  from  light  to  dark. 
In  the  display  of  data  arranged  by  classes  it  is  well  to  use 
different  patterns  or  colors.  Different  shades  may  be  ob- 
tained by  successive  washes  of  color  applied  with  a  brush, 
or  by  the  use  of  cross-hatching  in  which  the  proportion  of 
surface  covered  with  ink  regularly  increases.  The  so-called 
"  Ben  Day  "  system  of  indicating  shades  by  the  use  of 
special  devices  is  well  known  to  printers  and  engravers.1 

Sometimes  the  figures  themselves  are  placed  on  the  maps. 
If  this  is  done  care  should  be  taken  to  make  sure  that  the 
boundaries  of  the  areas  to  which  the  figures  apply  are  prop- 
erly defined. 

Blue  prints  and  other  prints.  —  It  is  often  desirable  to 
obtain  several  copies  of  the  diagrams  made,  and  the  quickest 
and  cheapest  method  is  that  of  making  blue  prints.  The 
process  is  the  same  as  that  of  making  photographic  prints 
from  a  negative.  Blue-print  paper  can  be  purchased;  in 
fact,  it  can  be  easily  made.  A  large  photographic  printing 
frame  is  required.  The  diagram  is  placed  in  the  frame  over 
the  blue-print  paper  and  exposed  to  the  sunlight  for  a 
few  minutes,  after  which  the  paper  is  washed  in  water  and 
dried.  It  is  necessary,  of  course,  to  have  the  paper  on 
1  See  Brinton's  Graphic  Methods,  pp.  216,  233. 


REPRODUCTION  OF  DIAGRAMS  97 

which  the  diagram  is  made  fairly  thin  and  transparent. 
Paper  should  be  selected  with  blue-printing  in  mind.  The 
transparency  of  paper  can  be  greatly  increased  by  oiling  it 
on  the  back  after  the  diagram  is  made.  A  liquid  sold 
under  the  name  of  "  transparantine  "  is  satisfactory.  The 
best  blue  prints  of  diagrams  are  obtained  by  the  use  of  trac- 
ing cloth.  This  has  many  advantages.  It  is  easy  to  ink 
on  and  erasures  may  be  made.  The  lines  are  sharp  and 
photograph  well.  The  cloth  does  not  tear.  The  cloth  is 
oiled  on  one  side.  The  drawing  should  be  done  on  the  other. 
A  little  powdered  chalk  should  be  dusted  on  and  rubbed  off 
before  using  ink.  Pencil  lines  may  be  used  as  guide  lines 
and  erased  before  blue-printing. 

In  the  ordinary  blue  print  the  lines  are  white  and  the 
background  blue.  Additional  white  lines  can  be  drawn  on 
the  blue  by  using  a  weak  solution  of  caustic  soda  in  a  pen 
as  ink. 

It  is  possible  to  .obtain  prints  in  which  blue  or  brown 
lines  appear  on  a  white  ground.  This  requires  the  making 
of  a  negative,  from  which  subsequent  prints  are  made. 

Reproduction  of  diagrams.  —  The  common  method  of 
reproducing  diagrams  for  publication  is  to  photograph  them 
and  print  from  a  zinc  plate.  This  is  the  cheapest  and  most 
available  method.  It  is  necessary  that  the  original  draw- 
ing be  well  made,  with  lines  of  the  right  weight  and  the 
letters  of  the  right  size.  All  imperfections  are  of  course 
reproduced.  Usually  the  drawing  should  be  made  at  least 
fifty  per  cent  larger  than  the  published  plate,  that  is,  the  size 
is  reduced  one-third.  To  have  diagrams  made  by  a 
draughtsman  costs  something,  but,  if  the  photographic 
process  is  to  be  used,  it  is  worth  while.  The  draughtsman 
should  know  what  the  size  of  the  published  plate  is  to  be. 

Those  not  skilled  in  making  diagrams  ought  to  know  that 
there  is  another  process  of  reproduction  which  does  not 


98  STATISTICAL  GRAPHICS 

require  a  carefully  drawn  original,  namely,  that  of  wax 
engraving.  In  this  process  the  engraver  does  the  work  of 
the  draughtsman.  A  copper  plate  is  used.  The  lettering 
in  this  process  can  be  put  in  with  type.  This  results  in  per- 
fect legibility,  which  is  often  not  the  case  with  photographic 
work.  Reproduction  by  the  wax  process  costs  almost 
twice  that  by  the  photographic  process,  but  if  to  the 
latter  is  added  the  time  and  expense  of  preparing  a  perfect 
original  the  wax  process  costs  no  more.  Most  of  the  plates 
in  this  book  were  made  by  the  wax  process  by  the  L.  L. 
Poates  Company  of  New  York.  Unfortunately  there  are 
not  many  wax  engravers  in  this  country. 

Equation  of  a  curve.  —  Having  plotted  certain  data  on 
rectangular  coordinate  paper,  that  is,  using  a  horizontal 
and  a  vertical  scale,  and  finding  that  the  points  fall  on  a 
straight  line  or  on  a  regular  curve,  it  is  sometimes  desirable 
to  find  the  equation  of  the  straight  line  or  curve.  This  is 
not  difficult,  but  it  requires  the  use  of  mathematical  prin- 
ciples not  considered  in  this  book.  The  reader  is  referred 
to  such  books  as  Saxelby's  "A  Course  in  Practical  Mathe- 
matics" x  or  Peddles'  " Construction  of  Graphical  Charts."2 


EXERCISES  AND    QUESTIONS 

1.  Describe  Ripley's  method  of  preparing  statistical  maps  with 
different  shadings.     [Pub.  Am.  Sta.  Asso.,  Sept.  1899,  pp.  319-322.] 

2.  Construct  a  graph  of  the  birth-rates  and  death-rates  of  Sweden 
from  1749  to  1900.     (See  p.  203.) 

3.  Construct  a  graph  of  the  natural  rate  of  increase  of  the  population 
of  Sweden  from  1749  to  1900. 

4.  Show  by  suitable  diagrams  the  data  in  Tables  100,  106  and  110. 

5.  Find  diagrams  in  this  book  which  do  not  conform  to  the  principles 
described  in  Chapter  III. 

1  Pub.  by  Longmans,  Green  &  Co.,  1908. 

2  Pub.  by  McGraw-Hill  Book  Co.,  1910, 


EXERCISES  AND 


99 


6.  Construct  a  "  devil's  Checker-board,"  as  follows: 

a.  Take  a  piece  of  cardboard  or  heavy  drawing  paper  and  rule  in 
black  ink  a  rectangle  8£"  wide  and  II"  high.     Rule  also  a  horizontal 
line  1"  below  the  top,  and  a  vertical  line  1"  from  left-hand  edge,  hi  order 
to  leave  suitable  margins  at  top  and  left. 

b.  Subdivide  the  1\"  on  the  horizontal  line  into  15  half-inch  spaces 
and  rule  vertical  lines.     Subdivide  the  10"  on  the  vertical  line  into  40 
quarter-inch  spaces  and  rule  horizontal  lines. 

c.  Draw  in  red  inclined  lines  sloping  downward  to  the  left,  being  \n 
apart  hi  a  horizontal  line  and  1^"  apart  in  a  vertical  direction. 

If  the  work  is  done  accurately  certain  of  these  diagonals  will  intersect 
corners  of  the  small  rectangles;  if  the  work  is  not  accurate  the  name  of 
the  problem  is  justified.  These  guide  lines  will  be  found  convenient  in 
the  construction  of  tables.  The  sloping  lines  will  serve  as  guides  for 
sloping  letters. 

7.  Construct  a  colored  wall  chart  showing  the  death-rates  from 
several  diseases  for  some  city,  using  the  one-scale  type  of  diagram. 
Assume  the  chart  is  to  be  read  from  a  distance  of  twenty  feet. 

8.  Describe  the  method  of  construction  and  the  varied  uses  of  ratio 
cross-section  paper.     (Quar.  Pub.  Am.  Sta.  Asso.     June,  1917,  p.  577.) 

9.  Plot  the  population  of  some  city  (assigned  by  the  instructor)  using 
ordinary  cross-section  paper  and  ratio  paper. 

10.  Construct  a  colored  component-part  diagram  (subdivided  circle), 
showing  the  composition  of  the  population  of  some  city  or  state  (data 
assigned  by  the  instructor). 


CHAPTER  IV 
ENUMERATION   AND   REGISTRATION 

All  civilized  nations  at  regular  periods  enumerate  their 
populations,  that  is,  take  a  census.  There  are  various 
governmental  reasons  for  doing  this,  two  important  ones 
being  the  adjustment  of  representation  in  legislative  bodies 
and  the  levying  of  taxes.  -There  are  also  business,  social 
and  sanitary  uses  to  which  the  figures  are  put.  In  consid- 
ering a  census  several  questions  immediately  arise;  when 
was  it  made,  what  area  was  included,  how  were  the  data 
obtained,  what  were  the  results  and  where  may  they  be 
found? 

The  United  States  census.  —  The  first  general  census  of 
the  United  States  was  made  in  1790,  the  first  year  divisible 
by  ten  after  the  founding  of  the  new  republic,  and  a  census 
has  been  taken  every  ten  years  since  that  date,  the  census 
of  1910  being  the  thirteenth. 

The  first  twelve  censuses  were  made  by  special  commis- 
sions created  for  the  purpose  and  which  went  out  of  exist- 
ence as  soon  as  the  task  had  been  accomplished.  A  per- 
manent Bureau  of  the  Census  was  created  in  1902.  At 
first  it  was  under  the  Department  of  the  Interior,  but  in 
1903  was  transferred  to  the  Department  of  Commerce  and 
Labor.  Its  head  is  known  as  the  Director  of  the  Census. 
Besides  taking  the  general  census  of  the  country  every 
ten  years  this  bureau  is  charged  with  the  collection  of  sta- 
tistics of  many  kinds  relating  to  the  people,  vital  statistics, 
financial  statistics,  municipal  statistics,  statistics  of  agri- 

100 


THE  UNITED  STATES  CENSUS  101 

culture,  fishing,  manufacture,  transportation,  mining,  and 
others. 

The  census  data  prior  to  1910  were  published  as  a  series 
of  special  volumes  by  the  commission  having  the  work  in 
charge.  Many  of  the  older  volumes  are  out  of  print,  but 
may  be  found  in  large  libraries.  In  1900  there  were  three 
volumes  on  population  and  two  volumes  on  vital  statistics 
obtainable  by  purchase  from  the  U.  S.  Publication  Office  at 
Washington.  Bulletins  of  the  census  of  1910  may  be  ob- 
tained from  the  "  Director  of  the  Census,  Washington, 
D.  C."  Lists  of  available  reports  and  bulletins  may  be 
obtained  without  charge  by  writing  to  the  director. 

In  1910  the  report  of  population  comprised  four  large 
volumes.  The  first  contained  the  general  data  for  the  coun- 
try, classified  and  grouped  in  many  ways;  the  second  and 
third  gave  the  population  subdivided  by  civil  divisions; 
the  fourth,  occupations.  For  some  time  it  has  been  cus- 
tomary to  include  in  each  census  report  the  populations  for 
the  two  censuses  preceding.  This  is  for  comparison  and  to 
enable  estimates  of  population  to  be  made.  Thus,  in  the 
thirteenth  census  will  be  found  the  populations  for  1910, 
1900  and  1890. 

A  table  often  consulted  was  that  on  page  430  of  Vol.  I, 
Part  I,  of  the  U.  S.  Census  of  1900,  which  gave  the  popula- 
tions of  all  cities  which  were  larger  than  25,000  in  1900,  for 
every  census  since  1790.  In  .the  1910  census  these  figures  are 
given  in  the  second  and  third  volumes  mentioned  under  the 
head  of  each  state.  See  also  pages  80-97  of  the  first  volume. 

These  census  reports  should  be  in  every  public  library, 
and  in  the  library  of  every  city  government,  as  they  con- 
tain a  vast  amount  of  important  information  relative  to 
the  growth  and  condition  of  our  country.  Every  student 
of  demography  should  become  thoroughly  familiar  with 
the  U.  S.  Census  reports. 


102  ENUMERATION  AN.D.  REGISTRATION 


The  census  date.  —  £or  most  purposes  it  is  sufficiently 
accurate  to  say  that  the  census  was  taken  in  a  certain 
year,  but  for  the  more  exact  computations  a  definite  day 
must  be  named.  The  population  of  the  country  is  con- 
stantly changing,  even  from  hour  to  hour.  If  we  wish  to 
use  the  figure  which  best  represents  the  population  for 
any  year  we  should  naturally  choose  the  population  as  it 
was  at  the  middle  of  the  year,  namely  July  1st.  But  it  is 
not  practicable  to  enumerate  all  of  the  people  on  a  single 
day,  and  July  1st  is  not  the  best  time  to  make  the  enumer- 
ation because  being  in  the  vacation  season  many  people 
are  likely  to  be  away  from  home.  For  practical  reasons 
another  day  is  chosen  as  the  official  day  for  taking  the 
census. 

In  1910  this  day  was  April  15th.  It  took  several  weeks 
to  make  the  enumeration,  but  the  data  were  adjusted  to 
this  day  so  that  the  statistics  are  stated  "  as  of  April  15th." 
But  it  should  be  noted  that  in  1900,  in  1890,  and  back  to 
1830  the  official  date  was  June  1.  Hence  between  the 
census  of  1900  and  1910  the  interval  was  not  10  years,  but 
ten  years  less  1J  months  (April  15  to  June  1)  or  1|  per  cent 
less  than  ten  years.  In  same  computations  this  introduces 
an  appreciable  error  and  a  correction  must  be  made.  From 
1820  back  to  1790  the  day  of  the  census  was  the  first  Mon- 
day in  August. 

In  Great  Britain,  including  Canada  and  Australia,  the 
national  census  is  taken  every  ten  years,  but  one  year  later 
than  in  the  United  States,  that  is,  in  1901  and  1911.  This 
has  been  so  since  1801.  The  time  of  the  census  is  "  at  mid- 
night before  the  first  Monday  in  April." 

It  is  quite  possible  to  adjust  the  population  of  the  census 
year,  1910,  so  as  to  find  what  it  was  on  July  1st  of  that  year, 
and  this  has  been  done  by  the  U.  S.  Census  Bureau  and  the 
figures  used  for  the  computation  of  mortality  statistics  for 


THE  ENUMERATION  SCHEDULE  OF  1910         103 

that  year.  The  method  used  is  described  in  the  next 
chapter. 

Civil  divisions.  —  The  population  of  the  United  States  is 
given  in  the  census  report's  by  minor  civil  divisions.  The 
total  population  of  the  nation  is  subdivided  into  continen- 
tal and  "  non-contiguous  territory,"  the  latter  including 
Alaska,  the  Hawaiian  Islands,  Porto  Rico,  and  persons  in 
naval  and  military  service  stationed  abroad.  The  con- 
tinental population  is  subdivided  into  states;  the  states 
into  counties;  the  counties  into  cities,  boroughs  or  towns; 
the  cities  into  wards;  the  boroughs  and  towns  into  villages 
and  rural  regions.  These  civil  divisions  differ  somewhat 
in  different  parts  of  the  country. 

In  comparing  the  figures  for  different  decades  it  must  be 
remembered  that  the  boundaries  of  the  civil  divisions-  are 
subject  to  change.  State  boundaries  are  quite  permanent, 
but  cities  frequently  increase  by  annexation  of  suburbs, 
and  ward  lines  change  still  more  frequently  according 
to  political  exigencies.  In  most  cases  changes  of  bound- 
aries are  indicated  in  the  census  reports  by  explanatory 
notes. 

In  sending  to  the  Director  of  the  Census  for  reports  of 
populations  by  states  or  for  the  whole  country,  the  request 
should  be  made  for  that  report  which  gives  the  facts  by 
"  minor  civil  divisions." 

The  enumeration  schedule  of  1910.  —  In  taking  the 
census  of  1910  the  country  was  divided  into  329  supervisor's 
districts  each  under  the  charge  of  a  supervisor  appointed 
by  the  President.  About  70,000  enumerators  were  selected 
by  the  supervisors,  or  one  for  about  every  1600  persons. 
The  enumerators  were  required  to  visit  each  dwelling  and 
collect  the  various  statistics  included  in  the  schedule. 

The  enumerators  began  their  work  throughout  the 
country  on  April  15,  1910.  The  law  provided  that  this 


104  ENUMERATION  AND  REGISTRATION 

should  be  completed  within  two  weeks  in  cities  of  5000  or 
more  inhabitants,  and  within  30  days  elsewhere. 

The  schedule  of  facts  to  be  collected  was  printed  on  sheets 
of  paper,  16  by  23  in.,  on  which 'were  100  horizontal  lines, 
50  on  each  side,  arxd  numbered  from  1  to  100.  The  facts 
for  each  person  occupied  one  line.1 

The  schedule  corresponded  closely  to  those  used  in  the 
censuses  from  1850  to  1880  and  1900.  The  schedule  used 
in  1890  was  somewhat  different,  a  separate  schedule  sheet 
15  by  11  in.  being  employed  for  each  family.2 

For  purposes  of  compilation  the  facts  for  each  person 
were  transferred  to  a  separate  punched  card.  These  cards 
were  then  sorted  by  machine. 

The  data  collected  by  the  enumerators  for  each  person 
were  as  follows : 

At  the  top  of  each  sheet  were  given  the  state,  county, 
township  or  other  division  of  county,  name  of  incorporated 
place,  name  of  institution  (if  any),  ward  of  city,  number  of 
supervisor's  district,  number  of  enumerator's  district,  name 
of  enumerator  and  date  of  enumeration.  - 


SCHEDULE 
Location. 

Street,  avenue,  road,  etc. 

House  number  (in  cities  or  towns). 

1.  Number  of  dwelling-house  in  order  of  visitation. 

2.  Number  of  family  in  order  of  visitation. 

3.  Name  of  each  person  whose  place  of  abode  on  Apr.  15, 1910  was  in 
this  family.     [Enter  surname  first,  then  the  given  name  and  middle 
initial,  if  any.     Include  every  person  living  on  Apr.  15,  1910.     Omit 
children  born  since  Apr.  15,  1910]. 

4.  Relation.     Relationship  of  this  person  to  the  head  of  the  family. 

1  U.  S.  Census,  1910,  Population,  Vol.  I,  p.  1368. 

2  U.  S.  Census,  1890,  Population,  Part  I,  CCIV. 


THE  ENUMERATION  SCHEDULE  OF  1910         105 

Personal  Description. 

5.  Sex. 

6.  Color  or  race. 

7.  Age  at  last  birthday. 

8.  Whether  single,  married,  widowed  or  divorced. 

9.  Number  of  years  of  present  maniage. 
Mother  of  how  many  children?    • 

10.  Number  born. 

11.  Number  now  living. 
Nativity. 

Place  of  birth  of  each  person  and  parents  of  each  person  enumerated. 
If  born  in  the  United  States  give  the  State  or  Territory.  If  of  foreign 
birth  give  the  country. 

12.  Place  of  birth  of  this  person  (including  mother  tongue). 

13.  Place  of  birth  of  father  of  this  person  (including  mother  tongue). 

14.  Place  of  birth  of  mother  of  this  person  (including  mother  tongue) . 
Citizenship. 

15.  Year  of  immigration  to  the  United  States. 

16.  Whether  naturalized  or  alien. 

17.  Language.    Whether  able  to  speak  English;    or,  if  not,  give 
language  spoken. 

Occupation. 

18.  Trade  or  profession  of,  or  particular  kind  of  work  done  by,  this 
person,  as  spinner,  salesman,  laborer,  etc. 

19.  General  nature  of  industry,  business  or  establishment  in  which 
this  person  works,  as  cotton  mill,  dry-goods,  store,  farm,  etc. 

20.  Whether  an  employer,  employee,  or  working  on  own  account. 
If  an  employee, 

21.  Whether  out  of  work  on  Apr.  15,  1910. 

22.  Number  of  weeks  out  of  work  during  year  1909. 

Education. 

23.  Whether  able  to  read. 

24.  Whether  able  to  write. 

25.  Attended  school  any  time  since  Sept.  1,  1909. 
Ownership  of  Home 

26.  Owned  or  rented. 

27.  Owned  free  or  mortgaged. 

28.  Farm  or  house. 

29.  Number  of  farm  schedule. 


106  ENUMERATION  AND  REGISTRATION 

Miscellaneous. 

30.  Whether  a  survivor  of  the,  Union  or  Confederate  Army  or  Navy. 

31.  Whether  blind  (both  eyes). 

32.  Whether  deaf  or  dumb. 

One  has  only  to  read  over  this  list  to  see  the  importance 
of  statistical  definitions.  •  What,  for  example,  is  meant  by 
the  "  usual  place  of  abode"?  This  is  the  place  where  he 
"lives"  or  " belongs  "  or  "the  place  which  is  his  home." 
As  a  rule  it  is  where  he  regularly  sleeps.  And  then  what 
about  those  persons  who  have  no  place  of  abode,  lodgers 
in  one-night  lodging  houses,  tramps,  laborers  in  construction 
camps,  etc.?  Such  persons  have  to  be  enumerated  where 
found.  It  required  a  formidable  book  of.  instructions  to 
make  all  these  things  plain  to  the  enumerators. 

Bowley's  rules  for  enumeration.  —  The  English  statis- 
tician, Bowley,  has  laid  down  the  following  rules  in  regard 
to  the  collection  of  statistical  data  by  the  method  of  enu- 
meration. 

"  In  practice  the  enumerator  is  usually  furnished  with 
blanks  to  be  filled  out  and  with  questions  to  be  answered. 
These  questions  should  be : 

1.  Comparatively  few  in  number. 

2.  Require  an  answer  of  a  number  or  of  a  "yes"  or  "no." 

3.  Simple  enough  to  be  readily  understood. 

4.  Such  as  will  be  answered  without  bias. 

5.  Not  unnecessarily  inquisitorial. 

6.  As  far  as  possible  corroboratory. 

7.  Such  as  directly  and  unmistakably  cover  the  point  of  information 
desired. 

These  rules  apply  equally  well  to  the  collection"  of  data 
by  registration." 

Credibility  of  census  returns.  —  It  is  not  to  be  expected 
that  the  census  figures  are  strictly  accurate.  Errors  are 
bound  to  be  made  by  the  enumerators;  some  persons  are 


COLLECTION  OF  FACTS  107 

sure  to  be  omitted  from  the  count,  especially  those  travel- 
ing; some  may  be  counted  twice;  and  in  rare  instances  the 
lists  have  been  thought  to  be  padded.  Taken  as  a  whole, 
however,  the  results  may  be  considered  as  reliable,  and  it 
should  be  noted  that  the  published  data  of  the  U.  S.  Census 
are  accepted  as  evidence  which  may  be  introduced  without 
proof  in  courts  of  record.  Unless  there  is  good  reason 
for  doing  otherwise  they  should  be  used  instead  of  local 
estimates  as  the  basis  of  computing  vital  rates.  As  a  rule 
also  they  should  be  used  in  place  of  state  censuses,  but 
there  are  some  exceptions  to  this. 

Collection  of  facts  by  registration  and  notification.  — 
If  it  is  difficult  to  secure  accurate  statistics  of  population 
obtained  by  enumerators  hired  for  the  purpose  and  properly 
instructed,  how  much  greater  the  difficulty  to  obtain  com- 
plete and  accurate  statistics  by  the  method  of  registration, 
when  the  returns  are  made  by  large  numbers  of  physicians, 
undertakers,  clergymen,  nurses  and  laymen  not  properly 
instructed,  not  interested  in  the  proceedings  and  not  always 
understanding  the  law,  with  inadequate  laws,  and  with 
governments  too  easy-going  to  insist  on  the  enforcement  of 
such  laws  as  exist!  And  yet  most  of  the  vital  statistics  of 
the  country  are  collected  in  this  way.  Worst  of  all,  the 
people  at  large  do  not  appreciate  the  personal  importance 
of  having  the  most  important  events  in  their  lives,  —  birth, 
marriage  and  death,  —  made  matters  of  public  record. 

By  registration  is  meant  the  reporting  of  certain  events 
and  associated  facts  to  a  governmental  authority  and  the 
official  filing  or  recording  of  such  facts.  The  reports  are 
made  in  accordance  with  prescribed  rules  and  usually  on 
a  blank  designed  for  the  purposes. 

Most  nations  in  one  way  or  another  have  endeavored  to 
preserve  their  history  by  keeping  these  personal  records. 
In  England  the  registration  of  baptisms,  marriages  and 


108  ENUMERATION  AND  REGISTRATION 

deaths  dates  back  to  1538  when  Thomas  Cromwell,  Vicar 
General  under  Henry  VIII,  issued  injunctions  to  all  parishes 
in  England  and  Wales  requiring  the  clergy  to  enter  every 
Sunday,  in  a  book  kept  for  the  purpose,  a  record  of  all 
baptisms,  marriages  and  burials  of  the  preceding  week. 
In  1653  this  work  was  assigned  to  "  parish  registers. " 
It  was  not  until  1837  that  registration  of  births,  marriages 
and  deaths  became  a  civil  function.  In  1870  it  was  made 
compulsory.  In  parts  of  Canada  the  registration  of  births 
and  deaths  is  still  on  a  parish  instead  of  a  civil  basis. 

In  the  early  American  colonies  the  practice  of  recording 
births,  marriages  and  deaths  was  instituted.  In  New 
England  the  town  clerk  figured  largely.  In  Massachusetts 
a  fairly  definite  law  was  passed  in  1692,  according  to  which 
the  town  clerk  was  required  to  keep  such  records,  and  there 
were  fees  to  be  paid  him  for  so  doing,  and  penalties  for 
those  persons  who  withheld  the  desired  information.  This 
act  was  altered  in  1795.  In  1842  a  registration  act  was 
passed  in  Massachusetts  which  made  the  Secretary  of  the 
Commonwealth  the  custodian  of  these  records.  This  act, 
together  with  an  amplifying  act  in  1844,  forms  the  basis  of 
registration  in  Massachusetts  to  this  day.  It  was  brought 
about  largely  through  the  activities  of  Lemuel  Shattuck.1 

The  story  of  the  registration  of  vital  statistics  is  too  long 
to  be  told  here.  Many  physicians,  like  Dr.  Edward  Jarvis, 
of  Boston,  -and  many  committees  of  such  organizations  as 
the  American  Medical  Association  and  the  American  Public 
Health  Associations  have  played  prominent  parts  in  the 
movement.  At  the  present  time  the  United  States  Bureau 
of  the  Census  is  taking  the  lead  in  urging  necessary  reforms 
in  the  registration  of  vital  statistics. 

The  laws  relating  to  the  registration  of  vital  statistics  are 
not  the  same  in  all  states.  In  Massachusetts  a  State  Reg- 
1  State  Sanitation,  by  George  C.  Whipple,  Vol.  I,  p.  56. 


REGISTRATION  OF  BIRTHS  109 

istrar  in  the  office  of  the  Secretary  of  the  Commonwealth 
has  charge  of  the  matter,  but  in  many  states  the  State 
Board  (or  Department)  of  Health  has  charge.  In  order  to 
bring  about  uniformity  a  model  law  was  drafted  and  en- 
dorsed by  a  number  of  national  organizations  and  this  has 
been  adopted  by  a  number  of  states.  Some  of  the  older 
states,  however,. still  maintain  their  old  arrangement.  This 
model  law  should  be  carefully  studied.  It  may  be  found  in 
the  Appendix. 

Registration  of  births.  —  It  is  important  that  the  birth 
of  each  and  every  child  born  be  duly  registered. 

The  information  desired  for  the  legal,  social  and  sanitary 
purposes,  according  to  the  United  States  standard  certifi- 
cate approved  by  the  Bureau  of  the  Census,  and  in  use  since 
1906,  is  as  follows: 

1.  Place  of  birth,  including  State,  county,  township  or  town,  village, 
or  city.     If  in  a  city,  the  ward,  street  and  house  number;  if  in  a  hospital 
or  other  institution,  the  name  of  the  same  to  be  given,  instead  of  the 
street  and  house  number. 

2.  Full  name  of  child.     If  the  child  dies  without  a  name,  before  the 
certificate  is  filed,  enter  the  words  "Died  unnamed."     If  the  living 
child  has  not  yet  been  named  at  the  date  of  filing  certificate  of  birth, 
the  space  for  "Full  name  of  child"  is  to  be  left  blank,  to  be  filled  out 
subsequently  by  a  supplemental  report,  as  hereinafter  provided. 

3.  Sex  of  child. 

4.  Whether  a  twin,  triplet,  or  other  plural  birth.     A  separate  cer- 
tificate shall  be  required  for  each  child  in  case  of  plural  births. 

5.  For  plural  births,  number  of  each  child  in  order  of  birth. 

6.  Whether  legitimate  or  illegitimate.     (This  question  may  be  omit- 
ted if  desired,  or  provision  may  be  made  so  that  the  identity  of  parents 
will  not  be  disclosed.) 

7.  Date  of  birth,  including  the  year,  month  and  day. 

8.  Full  name  of  father. 
9    Residence  of  father. 

10.  Color  or  race  of  father. 

11.  Age  of  father  at  last  birthday,  in  years. 

12.  Birthplace  of  father;  at  least  State  or  foreign  country,  if  known. 


110  ENUMERATION  AND  REGISTRATION 

s* 

13.  Occupation  of  father.     The  occupation  to  be  reported  if  engaged 
in  any  remunerative  employment,  with  the  statement  of   (a)   trade, 
profession,  or  particular  kind  of  work;    (6)  general  nature  of  industry, 
business,  or  establishment  in  which  employed  (or  employer). 

14.  Maiden  name  of  mother. 

15.  Residence  of  mother. 

16.  Color  or  race  of  mother. 

17.  Age  of  mother  at  last  birthday,  in  years. 

18.  Birthplace  of  mother;  at  least  State  or  foreign  country,  if  known. 

19.  Occupation  of  mother.     The  occupation  to  be  reported  if  en- 
gaged in  any  remunerative  employment,  with  the  statement  of  (a) 
trade,  profession,  or  particular  kind  of  work;    (&)  general  nature  of 
industry,  business,  or  establishment  in  which  employed  (or  employer). 

20.  Number  of  children  born  to  this  mother,  including  present  birth. 

21.  Number  of  children  of  this  mother  living. 

The  duty  of  making  out  this  certificate  rests  upon  the 
attending  physician,  mid-wife  or  person  acting  as  such, 
or  in  their  absence  upon  the  father  or  mother  of  the  child, 
the  householder  or  owner  of  the  premises  where  the  birth 
occurred  or  the  manager  or  superintendent  of  the  institu- 
tion, public  or  private,  where  the  birth  occurred,  each  in  the 
order  named.  This  certificate  must  be  filed  with  the  local 
registrar  within  ten  days  after  the  date  of  the  birth.  A 
supplemental  blank  is  provided  in  case  the  child  has  not 
been  named  when  the  first  report  is  submitted.  The  local 
registrar,  or  a  sub-registrar,  must  examine  this  certificate 
as  to  completeness  and  probable  accuracy,  secure  correc- 
tions if  necessary,  keep  a  record  of  the  birth  certificates 
received,  numbered  serially  as  received,  and  once  a  month 
transmit  the  original  certificates  to  the  State  Registrar,  for 
permanent  preservation.  Small  fees  to  local  registrars  for 
the  recording  of  births  are  provided  and  likewise  penalties 
for  failure.  Provision  is  made  for  giving  certified  copies  of 
the  birth  records  to  persons  entitled  to  receive  them. 

The  period  of  time  within  which  a  birth  must  be  recorded 
may  with  advantage  be  less  than  the  ten  days  above  men- 


ENFORCEMENT  OF  THE  REGISTRATION  LAW      111 

tioned,  especially  in  cities,  in  fact  it  is  best  that  the  birth 
be  reported  within  twenty-four  hours.  If,  as  should  be 
the  case,  the  local  registrar  is  connected  or  closely  associ- 
ated with  the  local  board  of  health,  the  prompt  information 
that  a  birth  has  occurred  enables  the  health  officer  to  send 
a  visiting  nurse  to  offer  advice  and  assistance  in  caring  for 
the  child.  Infant  mortality  cannot  be  greatly  reduced  in 
cities  unless  this  prompt  report  is  made. 

Advantages  to  individuals  of  having  births  publicly 
recorded.  —  Legal  evidence  is  thus  made  available  as  to:  — 

Place  of  Birth,  useful  to  prove  citizenship  (necessary  for 
pass-ports),  to  prove  residence,  to  acquire  a  legal  "  settle- 
ment." 

Time  of  Birth,  useful  to  prove  age,  to  obtain  admission 
to  school,  to  establish  right  to  go  to  work  (legal  age),  to 
prove  liability  for  military  service,  to  establish  right  to  vote, 
to  obtain  pensions. 

Parentage,  to  prove  legitimacy,  to  inherit  property,  to 
obtain  settlement  of  insurance,  to  establish  citizenship. 

What  are  some  of  the  evidences  of  incomplete  birth 
registration?  —  Dr.  Louis  I.  Dublin  has  suggested  three 
simple  tests.  First.  The  number  of  births  registered  in  a 
calendar  year  should  be  greater  than  the  number  of  living 
children  under  one  year  of  age.  Second.  The  birth-rate 
does  not  usually  vary  greatly  from  year  to  year.  Wide 
and  erratic  variations  indicate  probable  deficiencies  in 
reporting.  Third.  Birth-rates  less  than  20  per  thousand 
(or  less  than  25  per  thousand  in  cities  which  have  large 
foreign  populations)  are  uncommon  where  registration  is 
complete. 

Enforcement  of  the  registration  law.  —  The  persons  most 
concerned  in  the  enforcement  of  the  birth  registration  law 
are  (1)  the  state  registrar,  who  should  be  associated  with 
the  state  department  of  health;  (2)  the  local  registrar,  who 


112  ENUMERATION   AND  REGISTRATION 

should  be  associated  with  the  local  board  of  health;  (3) 
the  physician,  whose  'duty  it  is  to  make  the  report;  and  (4) 
the  parents  of  the  child  and  the  child  himself  or  herself. 

In  order  that  better  registration  be  obtained  parents  and 
physicians  should  be  made  to  understand  the  benefits 
which  result  to  individuals  and  to  the  community.  Facili- 
ties in  the  form  of  suitable  blanks,  etc.,  should  be  provided, 
so  as  not  to  make  the  matter  of  reporting  a  burden  to  busy 
physicians.  It  might  well  be  that  a  simple  post-card 
notification,  stating  that  a  birth  occurred  at  such  and  such 
a  place,  sent  on  the  day  of  birth,  with  a  complete  certificate 
filed  at  a  later  date  would  help  to  solve  the  problem.  No 
fee  should  be  given  to  a  physician  who  does-  not  report 
within  the  statutory  time  limit.  What  is  most  needed 
however  is  a  rigid  enforcement  of  the  penalty  clause.  A 
local  registrar  once  gave  the  author  as  the  reason  for  not 
imposing  fines  on  physicians  for  failure  to  report,  —  "  I 
am  too  good  natured."  This  spirit  is  fatal  to  good  .govern- 
ment. 

Registrars  are  not  without  opportunity  to  obtain  evidence 
of  neglect.  In  the  case  of  reported  infant  deaths  the  local 
registrar  should  ascertain  if  the  child's  birth  had  been 
recorded.  Church  records  of  baptisms  may  be  compared 
with  birth  returns.  The  checks  are  not  as  complete  as  in 
the  case  of  death  returns,  but  an  ingenious  local  registrar 
will  have  little  difficulty  in  getting  good  returns  if  he  takes 
his  task  seriously. 

In  Cambridge,  Mass.,  the  birth  records  are  so  incomplete 
that  annually  a  house  to  house  canvass  is  made  to  ascer- 
tain the  births  for  the  year.  This  is  a  disgraceful  admis- 
sion of  incompetence  on  the  part  of  the  local  registrar  and 
of  the  negligence  of  all  concerned.  No  fines  are  imposed 
and  some  of  the  payments  of  fees  are,  with  a  proper  inter- 
pretation of  the  law,  of  questionable  legality.  Unfortu- 


REGISTRATION  OF  DEATHS  113 

nately  Cambridge  is  not  alone  in  this,  but  is  typical  of 
hundreds  of  other  cities. 

Registration  of  deaths.  —  The  facts  desired  in  connection 
with  deaths  are  as  follows,  according  to  the  United  States 
Standard  Certificate. 

1.  Place  of  death,  including  State,  county,  township,  village,  or  city. 
If  in  a  city,  the  ward,  street,  and  house  number;  if  in  a  hospital  or  other 
institution,  the  name  of  the  same  to  be  given  instead  of  the  street  and 
house  number.     If  in  an  industrial  camp,  the  name  of  the  camp  to  be 
given. 

2.  Full  name  of  decedent.     If  an  unnamed  child,  the  surname  pre- 
ceded by  "Unnamed." 

2a.  Residence  at  usual  place  of  abode  (ward,  street  and  number),  and 
length  of  residence  in  city  or  town  where  death  occurred  in  years  and 
months.  Also  how  long  in  United  States  if  of  foreign  birth. 

3.  Sex. 

4.  Color  or  race,  as  white,  black,  mulatto  (or  other  negro  descent), 
Indian,  Chinese,  Japanese,  or  other. 

5.  Conjugal  condition,  as  single,  married,  widowed,  or  divorced. 
5a.   If  married,  widowed,  or  divorced.     Name  of  husband  or  wife. 

6.  Date  of  birth,  including  the  year,  month,  and  day. 

7.  Age,  in  years,  months,  and  days.     If  less  than  one  day,  the  hours 
or  minutes. 

8.  Occupation.     The  occupation  to  be  reported  of  any  person,  male 
or  female,  who  had  any  remunerative  employment,  with  the  statement 
of  (a)  trade,  profession  or  particular  kind  of  work;   (6)  general  nature  of 
industry,  business,  or  establishment  in  which  employed  (or  employer) ; 
(c)  name  of  employer. 

9.   Birthplace;  at  least  State  or  foreign  country,  if  known. 

10.  Name  of  father. 

11.  Birthplace  of  father;  at  least  State  or  foreign  country,  if  known. 

12.  Maiden  name  of  mother. 

13.  Birthplace  of  mother;  at  least  State  or  foreign  country,  if  known. 

14.  Signature  and  address  of  informant. 

15.  Official  signature  of  registrar,  with  the  date  when  certificate  was 
filed,  and  registered  number. 

16.  Date  of  death,  year,  month,  and  day. 

17.  Certification  as  to  medical  attendance  on  decedent,  fact  and  time 
of  death,  time  last  seen  alive,  and  the  cause  of  death,  with  contribu- 


114  ENUMERATION  AND  REGISTRATION 

tory  (secondary)  cause  of  complication,  if  any,  and  duration  of  each, 
and  whether  attributed  to  dangerous  or  insanitary  conditions  of  em- 
ployment; signature  and  address  of  physician  or  official  making  the 
medical  certificate. 

18.  Where  was  the  disease  contracted  if  not  at  place  of  birth  ?     Did 
an  operation  precede  death  ?    If  so  give  date.     Was  there  an  autopsy  ? 
What  test  confirmed  diagnosis  ? 

19.  Place  of  burial  or  removal;  date  of  burial. 

20.  Signature  and  address  of  undertaker  or  person  acting  as  such. 

The  first  thirteen  items  are  chiefly  personal  and  these 
facts  may  be  signed  by  any  competent  person  acquainted 
with  the  facts.  Items  16  and  17  comprise  the  medical 
certificate,  which  must  be  made  out  by  the  physician, 
if  any,  last  in  attendance.  In  the  absence  of  medical 
attendance  the  undertaker  must  notify  the  local  registrar 
who  may  not  issue  a  burial  permit  until  the  case  is  referred 
to  the  local  health  officer  for  investigation  and  certifi- 
cation. In  case  there  is  suspicion  of  neglect  or  unlawful 
act  the  coroner,  medical  examiner,  or  other  proper  officer 
must  conduct  an  investigation.  There  are  various  provisos, 
differing  in  different  states,  which  should  be  known  by 
every  physician  and  nurse  and,  of  course,  by  every  health 
officer.  Finally  items  19  and  20  must  be  signed  by  the 
undertaker. 

The  certificate  of  death  thus  made  out  and  duly  signed 
must  be  filed  by  the  undertaker  with  the  local  registrar  (in 
some  states  the  local  board  of  health),  and  a  burial  permit 
or  removal  permit  obtained  prior  to  the  disposition  of  the 
body.  This  permit  must  be  delivered  before  burial  to  the 
person  in  charge  of  the  place  of  burial.  If  the  body  is 
transported  the  undertaker  must  attach  a  removal  permit 
to  the  box  containing  the  corpse  in  order  that  it  may  reach 
the  person  in  charge  of  the  place  of  burial. 

Thus  the  undertaker  is  primarily  responsible  for  filing 
the  certificate  with  the  local  registrar  (or  local  board  of 


MARRIAGE  REGISTRATION  115 

health),  but  the  physician  is  responsible  for  making  out 
certain  very  essential  parts  of  the  certificate. 

Records  of  death  certificates  and  burial  permits  are  of 
course  kept  by  the  local  registrar  (or  local  board  of  health). 
Thus  there  is  a  check  on  the  death  certificate,  and  partly 
for  this  reason  the  registration  of  deaths  is  more  complete 
than  the  registration  of  births.  It  is  easier  to  come  into  the 
world  without  public  notice  than  it  is  to  leave  it. 

The  data  regarding  the  deaths  are  transmitted  by  the 
local  registrar  to  the  state  registrar. 

Uses  of  death  registration.  —  The  uses  of  death  regis- 
tration are  legal,  economic,  and  social.  It  assists  in  the 
prevention  and  detection  of  crime.  It  is  invaluable  in  the 
settlement  of  life  insurance  and  property  inheritance  cases. 
It  furnishes  the  basis  of  genealogical  studies.  The  sta- 
tistics based  upon  these  records  have  been  a  powerful 
weapon  in  studying  disease,  and  therefore  in  improving 
the  health  of  the  race  and  lengthening  human  life.  The 
records  may  be  of  great  local  value  in  the  study  and  sup- 
pression of  epidemics  and  outbreaks  of  communicable  dis- 
eases. 

Marriage  registration.  -  -  There  is  no  uniform  or 
"  model  "  marriage  law  in  the  United  States;  state  laws 
differ  from  each  other.  The  custom  is  that  persons  desiring 
to  marry  must  first  obtain  a  civil  license  from  a  designated 
local  official  and  present  it  to  the  authorized  person  who 
performs  the  ceremony.  The  person  officiating  is  required 
to  register  the  marriage.  The  persons  responsible  for  mar- 
riage registration  are  therefore  the  clergymen  and  the 
justices  of  the  peace. 

The  facts  required  in  the  registration  of  marriages  are 
commonly  as  follows: 


116  ENUMERATION  AND  REGISTRATION 

1.  Date  of  the  marriage. 

2.  Place  of  the  marriage. 

3.  Names  of  the  persons  married. 

4.  Their  places  of  birth. 

5.  Their  residences. 
.    6.  Their  ages. 

7.  Their  color. 

8.  The  number  of  the  marriage  (as  the  first  or  second). 

9.  If  previously  married,  whether  widowed  or  divorced. 

10.  Their  occupations. 

11.  The  names  of  their  parents. 

12.  The  maiden  names  of  their  mothers. 

13.  The  date  of  the  record. 

14.  The  signature  of  the  officiating  person. 

15.  His  residence  and  official  station. 

Morbidity  registration.  —  The  compulsory  registration 
of  cases  of  disease  dangerous  to  the  public  health  is  com- 
paratively modern.  It  is  true  that  many  years  ago  such 
dreaded  diseases  as  smallpox  had  to  be  reported,  but  it  is 
since  the  organization  of  modern  health  departments  and 
the  general  understanding  of  the  manner  in  which  com- 
municable diseases  are  spread  that  compulsory  notification 
has  become  widespread.  In  1874  the  State  Board  of 
Health  of  Massachusetts  took  the  lead  by  arranging  a  plan 
for  the  weekly  voluntary  notification  of  prevalent  diseases. 
Over  a  hundred  physicians  agreed  to  make  this  report. 
Ten  years  later,  in  1884,  the  state  passed  a  law  requiring 
householders  and  physicians  to  report  immediately  to  the 
selectmen  or  board  of  health  of  the  town  all  cases  of  small- 
pox, diphtheria,  scarlet  fever,  or  any  other  disease  danger- 
ous to  the  public  health.  Other  states  followed  suit. 

The  requirement  of  notification  of  diseases  is  an  act  of 
police  power  and  authority  for  it  resides  in  the  state  gov- 
ernments. In  Massachusetts  legislative  authority  has  been 
delegated  to  the  State  Board  (now  Department)  of  Health 
to  determine  what  diseases  are  dangerous  to  the  public 


MORBIDITY  REGISTRATION  117 

health,  and  such  diseases  must  be  reported  according  to 
prescribed  rules.  Power  is  often  delegated  to  local  com- 
munities to  supplement  the  state  requirements  for  local 
reports.  At  the  present  time  the  regulations  in.  the  several 
states  differ  greatly  from  each  other. 

In  1913  a  model  law  for  morbidity -reports  was  adopted 
by  a  conference  of  state  and  territorial  health  authorities 
and  the  U.  S.  Public  Health  service.  According  to  this 
law  the  state  boards  (or  departments)  of  health  are  re- 
quired to  provide  machinery  for  keeping  informed  as  to 
current  diseases  dangerous  to  the  public  health;  physi- 
cians are  required  to  report  cases  of  such  diseases  imme- 
diately to  the  local  health  authorities  having  jurisdiction; 
teachers  in  schools  must  do  the  same;  these  records  must 
be  promptly  sent  to  the  state  authorities.  There  are  vari- 
ous provisos  and  provisions  for  keeping  records,  and  for 
penalties.  The  data  required  are  the  following: 

1.  The  date  when  the  report  is  made. 

2.  The  name  of  the  disease  or  suspected  disease. 

3.  Patient's  name,  age,  sex,  color,  and  address.     (This  is  largely  for 
purposes  of  identification  and  location.) 

4.  Patient's  occupation.     (This  serves  to  show  both  the  possible 
origin  of  the  disease  and  the  probability  that  others  have  been  or  may 
be  exposed.) 

5.  School  attended  by  or  place  of  employment  of  patient.     (Serves 
same  purpose  as  the  preceding.) 

6.  Number  of  persons  in  the  household,  number  of  adults  and  number 
of  children.     (To  indicate  the  nature  of  the  household  and  the  prob- 
able danger  of  the  spread  of  the  disease.) 

7.  The  physician's  opinion  of  the  probable  source  of  infection  or 
origin  of  the  disease.     (This  gives  important  information  and  frequently 
reveals  unreported  cases.     It  is  of  particular  value  in  occupational  dis- 
eases.) 

8.  If  the  disease  is  smallpox,  the  type  (whether  the  mild  or  virulent 
strain)  and  the  number  of  times  the  patient  has  been  successfully  vac- 
cinated, and  the  approximate  dates.     (This  gives  the  vaccination  status 
and  history.) 


118 


ENUMERATION  AND  REGISTRATION 


9.  If  the  disease  is  typhoid  fever,  scarlet  fever,  diphtheria,  or  septic 
sore  throat,  whether  the  patient  had  been  or  whether  any  member  of 
the  household  is  engaged  in  the  production  or  handling  of  milk.     (These 
diseases  being  frequently  spread  through  milk,  this  information  is  im- 
portant to  indicate  measures  to  prevent  further  spread.) 

10.  Address  and  signature  of  the  physician  making  the  report. 

Notifiable  diseases.  —  The  following  was  the  list  of  dis- 
eases made  notifiable  by  the  model  law  of  1913.  Obviously 
this  cannot  be  a  permanent  one.  It  is  being  continually 
revised  chiefly  by  addition.  In  many  states  influenza  has 
been  added  to  the  list  during  the  last  few  months  (1918). 
Under  present  conditions  the  lists  vary  in  different  states. 

GROUP  I.  —  INFECTIOUS  DISEASES. 


Actinomycosis. 

Anthrax. 

Chicken-pox. 

Cholera.     Asiatic    (also    cholera 

nostras    when  Asiatic   cholera 

is    present   or  its  importation 

threatened). 

Continued  fever  lasting  seven  days 
Dengue. 
Diphtheria. 
Dysentery : 

(a)  Amebic. 

(6)  Bacillary. 
Favus. 

German  measles. 
Glanders. 

Hookworm  disease. 
Leprosy. 
Malaria. 
Measles. 
Meningitis: 

(a)  Epidemic  cerebrospinal. 
(6)  Tuberculous. 
Mumps. 


Ophthalmia  neonatorum  (con- 
junctivitis of  new-born  infants). 

Paragonimiasis  (endemic  hemop- 
tysis). 

Paratyphoid  fever. 

Plague. 

Pneumonia  (acute). 

Poliomyelitis  (acute  infectious). 

Rabies. 

Rocky  Mountain  spotted,  or  tick, 
fever. 

Scarlet  fever. 

Septic  sore  throat. 

Smallpox. 

Tetanus. 

Trachoma. 

Trichinosis. 

Tuberculosis  (all  forms,  the  organ 
or  part  affected  in  each  case  to 
be  specified). 

Typhoid  fever. 

Typhus  fever. 

Wh6oping  cough. 

Yellow  fever. 


INCOMPLETENESS  OF  MORBIDITY  STATISTICS     119 

GROUP  II.  —  OCCUPATIONAL  DISEASES  AND  INJURIES. 

Arsenic  poisoning.  Bisulphide  of  carbon  poisoning. 

Brass  poisoning.  Dinitrobenzine  poisoning. 

Carbon  monoxide  poisoning.  Caisson  disease   (compressed-air 
Lead  poisoning.  illness). 

Mercury  poisoning.  Any  other  disease  or  disability 
Natural  gas  poisoning.  contracted  as  a  result  of  the 

Phosphorus  poisoning.  nature  of  the  person's  employ- 

Wood  alcohol  poisoning.  ment. 

Naphtha  poisoning. 

GROUP  III. — VENEREAL  DISEASES. 
Gonococcus  infection.  Syphilis. 

GROUP  IV.  —  DISEASES  OF  UNKNOWN  ORIGIN. 
Pellagra.  Cancer. 

Incompleteness  of  morbidity  statistics.  —  Complete  ac- 
curacy in  securing  records  of  morbidity  under  any  law  is 
impossible.  All  of  the  cases  existing  are  not  seen  by  physi- 
cians, of  the  cases  seen  not  all  are  recognized  or  correctly 
diagnosed,  of  those  recognized  not  all  are  reported  within 
the  required  time  and  some  not  at  all.  The  chief  error  is 
that  of  incompleteness.  Conservative  physicians  wait  until 
sure  of  their  diagnosis  before  reporting.  A  vast  number 
of  physicians  are  careless;  a  few  deliberately  shield  their 
patients  from  possible  inconvenience  by  withholding  re- 
ports. More  and  more,  however,  physicians  are  coming 
to  realize  that  in  dealing  with  communicable  diseases  they 
have  a  public  as  well  as  a  private  duty.  Death  certificates 
give  a  partial  check  on  morbidity  reports.  The  ratios  be- 
tween statistics  of  sickness  and  death  from  reportable  dis- 
eases furnishes  a  measure  of  the  incompleteness  of  the  re- 
ports. Trask  has  noted  this  difference  between  morbidity 
and  mortality  returns;  death  records  are  usually  com- 


120  ENUMERATION  AND  REGISTRATION 

plete  but  the  cause  of  death  often  incorrectly  diagnosed, 
morbidity  records  are  incomplete,  but  the  diagnosis  usu- 
ally correct.  This  must  be  kept  in  mind  in  dealing  with 
fatality  ratios. 

Morbidity  from  non-reportable  diseases.  —  It  is  much  to 
be  regretted  t;hat  at  the  present  time  there  is  no  adequate 
way  of  getting  the  facts  in  regard  to  sickness  in  the  com- 
munity due  to  diseases  which  are  non-reportable.  Sick- 
ness surveys  are  sometimes  made,  but  they  give  only  the 
facts  at  a  given  date,  and  are,  moreover,  very  expensive  to 
make.  Hospital  records  help  us  a  little,  the  examinations 
made  by  the  life  insurance  companies  help  a  little,  the  re- 
cent examinations  of  men  for  the  army  have  helped  a  good 
deal,  but  some  day  a  more  universal  method  must  be  de- 
vised. 

Reporting  venereal  diseases.  —  For  a  number  of  years 
the  matter  of  requiring  physicians  to  report  cases  of  vene- 
real diseases  as  diseases  dangerous  to  the  public  health 
has  been  under  consideration  by  public  health  officials; 
in  a  few  places  it  has  been  attempted.  The  present  war 
has  emphasized  the  need  of  such  reports  and  these  are 
now  required  in  many  states.  For  social  reasons  it  is  un- 
desirable to  have  the  names  of  the  victims  reported,  yet 
under  some  conditions  it  is  desirable  and  necessary  in  the 
control  of  disease.  The  following  system  was  adopted  by 
the  Massachusetts  State  Department  of  Health  in  1918  as  a 
war  measure. 

1.  Gonorrhrea  and  syphilis  are  declared  diseases  dan- 
gerous, to  the  public  health  and  shall  be  reported  in  the 
manner  provided  by  these  regulations  promulgated  under 
the  authority  of  chapter  670,  Acts  of  1913. 

2.  Gonorrhoea  and  syphilis  are  to  be  reported  (in  the 
manner  provided  by  these  regulations)  on  and  after  Feb.  1, 
1918. 


REPORTING  VENEREAL  DISEASES  121 

3.  At  the  time  of  the  first  visit  or  consultation  the  physi- 
cian shall  furnish  to  each  person  examined  or  treated  by 
him  a  numbered  circular  of  information  and  advice  con- 
cerning the  disease  in  question,  furnished  by  the  State 
Department  of  Health  for  that  purpose. 

4.  The  physician  shall  at  the  same  time  fill  out  the  num- 
bered report  blank  attached  to  the  circular  of  advice,  and 
forthwith  mail  the  same  to  the  State  Department  of  Health. 
On  this  blank  he  shall  report  the  following  facts: 

Name  of  the  disease. 

Age. 

Sex. 

Color. 

Marital  condition  and  occupation  of  the  patient. 

Previous  duration  of  disease  and  degree  of  infectiousness. 

The  report  shall  not  contain  name  or  address  of  patient. 

5.  Whenever   a   person   suffering   from    gonorrhoea   or 
syphilis  in  an  infective  stage  applies  to  a  physician  for  ad- 
vice or  treatment,  the  physician  shall  ascertain  from  the 
person  in  question  whether  or  not  such  person  has  pre- 
viously consulted  with  or  been  treated  by  any  other  njiysi- 
cian  within  the   Commonwealth.     If  not,   the   physician 
shall  give  and  explain  to  the  patient  the  numbered  circular 
of  advice,  as  provided  in  the  previous  regulation. 

If  the  patient  has  consulted  with  or  been  treated  by 
another  physician  within  the  Commonwealth  and  has  re- 
ceived th'e  numbered  circular  of  advice,  the  physician  last 
consulted  shall  not  report  the  case  to  the  State  Department 
of  Health,  but  shall  ask  the  patient  to  give  him  the  name 
and  address  of  the  physician  last  previously  treating  said 
patient. 

6.  In  case  the  person  seeking  treatment  for  gonorrhoea 
or  syphilis  gives  the  name  and  address  of  the  physician  last 
previously  consulted,  the  physician  then  being  consulted 


122  ENUMERATION  AND  REGISTRATION 

shall  notify  immediately  by  mail  the  physician  last  pre- 
viously consulted  of  the  patient's  change  of  medical  adviser. 

7.  Whenever  any  person  suffering  from  gonorrhoea  or 
syphilis  in  an  infective  stage  shall  fail  to  return  to  the 
physician  treating  such  person  for  a  period  of  six  weeks 
later  than  the  time  last  appointed  by  the  physician  for  such 
consultation  or  treatment,  and  the  physician  also  fails  to 
receive  a  notification  of  change  of  medical  advisers  as  pro- 
vided in  the  previous,  section,   the  physician  shall  then 
notify  the  State  Department  of  Health,  giving  name,  ad- 
dress of  patient,  name  of  the  disease  and  serial  number, 
date  of  report  and  name  of  physician  originally  reporting 
the  case  by  said  serial  number,  if  known. 

8.  Upon  receipt  of  a  report  giving  name  and  address  of  a 
person  suffering  from  gonorrhoea  or  syphilis  in  an  infective 
stage,  as  provided  in  the  previous  section,  the  State  De- 
partment of  Health  will  report  name  and  address  of  the 
person  as. a  person  suffering  from  a  disease  dangerous  to 
the  public  health,  and  presumably  not  under  proper  medi- 
cal advice  and  care  sufficient  to  protect  others  from  infec- 
tion,.to  the  board  of  health  of  the  city,  or  town  of  patient's 
residence  or  last  known  address.     The  State  Department  of 
Health  shall  not  divulge  the  name  of  the  physician  making 
said  report. 

Sickness  surveys.  —  A  new  method  of  securing  data  in 
regard  to  disease  has  been  recently  applied  in  an  experi- 
mental way  in  a  number  of  cities,  namely  that  of  'making  a 
house  to  house  canvas  to  determine  the  number  of  persons 
ill  at  the  time.  The  Metropolitan  Life  Insurance  Com- 
pany has  been  foremost  in  this  undertaking  under  the 
direction  of  Dr.  Lee  K.  Frankel  and  Dr.  Louis  I.  Dublin. 
Spring  and  fall  surveys  have  been  made  in  several  cities, 
the  enumerator  for  the  most  part  being  the  collecting 
agents  of  the  insurance  company. 


UNITED  STATES  REGISTRATION  AREA  FOR  DEATHS     123 

The  data  sheet  used  included  the  age,  sex,  and  occupa- 
tion of  each  member  of  the  family;  and  if  sick  the  disease 
or  cause  of  disability,  its  duration  and  extent,  i.e.,  whether 
confined  to  bed,  and  the  kind  of  treatment,  i.e.,  by  physi- 
cian at  home,  hospital,  or  dispensary. 

Surveys  have  been  made  for  Rochester,  N.  Y.,  September, 
1915;.  Trenton,  N.  J.,  October,  1915;  North  Carolina 
(sample  districts  throughout  the  state),  April,  1916;  Bos- 
ton, Mass.,  July,  1916;  Chelsea  neighborhood  of  New 
York  City,  April,  1917;  Pittsburg  and  other  cities  of 
Pennsylvania  and  West  Virginia,  March,  1917;  Kansas 
City,  Mo.,  April,  1917. 

This  method  obviously  has  its  advantages  and  disad- 
vantages. Within  its  natural  limitations  the  data  secured 
ought  to  be  of  value  and  should  furnish  an  excellent  check 
on  the  results  obtained  by  registration  of  communicable 
diseases. 

Other  methods  of  securing  data.  —  It  will  not  be  pos- 
sible to  describe  here  all  of  the  many  ways  in  which  data 
bearing  on  the  health  of  a  community  may  be  secured, 
but  mention  should  be  made  of  the  importance  of  hospital 
records,  life  insurance  records,  records  of  physical  exami- 
nations made  by  the  U.  S.  Army  and  Navy,  records  of 
physical  examinations  of  school  children.  More  and  more 
the  systematic  physical  examination  of  the  people  will  be 
extended,  until  it  becomes  universal  and  compulsory.  All 
of  this  will  wonderfully  increase  our  knowledge  of  vital 
statistics. 

United  States  registration  area  for  deaths.  —  The  Bureau 
of  the  Census  keeps  records  and  publishes  reports  of  the 
mortality  of  those  parts  of  the  United  States  where  the 
statistics  are  sufficiently  accurate  to  make  it  worth  while 
to  do  so.  A  so-called  registration  area  for  deaths  was  es- 
tablished in  1880.  This  included  those  states  and  cities 


124 


ENUMERATION  AND  REGISTRATION 


in  which  satisfactory  registration  laws  were  being  effec- 
tively enforced  and  where  there  was  good  reason  to  believe 
that  more  than  90  per  cent  of  all  deaths  were  being  regis- 
tered. At  first  the  registration  area  included  only  two  states, 
Massachusetts  and  New  Jersey,  and  certain  cities  in  other 
states.  The  area  has  gradually  expanded  as  shown  by  the 
following  tables.  In  studying  the  mortality  rates  of 
the  country  in  the  published  reports  it  is  important  to  keep 
in  mind  this  addition  of  new  territory,  new  populations, 
from  year  to  year. 

TABLE  19 
REGISTRATION  AREA  FOR  DEATHS 


Year. 

Population. 

Land  area. 

Number. 

Per  cent  of 
total. 

Square  miles. 

Per  cent  of 
total. 

(1) 

(2) 

(3) 

(4) 

(5) 

1880 

8,538,366 

17.0 

16,481 

0.6 

1890 

19,659,440 

31.4 

90,695^ 

3.0 

1900 

30,765,618 

40.5 

212,621 

7.1 

1901 

31,370,952 

40.3 

212,770 

7.2 

2 

32,029.815 

40.4 

212,762 

7.2 

3 

32,701,083 

40.4 

212,762 

7.2 

4 

33,345,163 

40.4 

212,744 

7.2 

5 

34,052,201 

40.4 

212,744 

7.2 

6 

41,983,419 

48.9 

603,066 

20.3 

7 

43,016,990 

49.2 

603,151 

20.3 

8 

46,789,913 

52.5 

725,117 

24.4 

9 

50,870,518 

56.1 

765,738 

25.7 

1910 

53,843,896 

58.3 

997,978 

33.6 

11 

59,275,977 

63.1 

1,106,734 

37.2 

12 

60,427,247 

63.2 

1,106,777 

37.2 

13 

63.298,718 

65.1 

1,147,039 

38.6 

14 

65,989,295 

66.8 

1,228,644 

41.3 

15 

67,336,992 

67.1 

1,228,704 

41.3 

16 

71,621,632 

70.2 

1,307,819 

44.0 

17 

75,306,588 

72.7 

1,349,506 

45.4 

18 

81,786,052 

77.7 

1,546,166 

52.0 

UNITED  STATES  REGISTRATION  AREA  FOR  DEATHS     125 


TABLE  20 

LIST  OF   STATES  IN  THE  REGISTRATION  AREA  FOR 
DEATHS 


Year  of 

Entrance. 

State. 

Year  of 
Entrance. 

State. 

(1) 

(2) 

(1) 

(2) 

1880 

Massachusetts 

1906 

South  Dakota  (drop- 

New Jersey 
District  of  Columbia 

1908 

ped  in  1910) 
Washington 

1890 

Connecticut 

Wisconsin 

Delaware  (dropped  in 

1909 

Ohio 

1900) 

1910 

Minnesota 

New  Hampshire 

Montana 

New  York 

Utah 

Rhode  Island 

1911 

Kentucky 

Vermont 

Missouri 

1900 

Maine 

1913 

Virginia 

Michigan 

1914 

Kansas 

Indiana 

1916 

North  Carolina 

1906 

California 

South  Carolina 

Colorado 

1917 

Tennessee 

Maryland 

.1918 

Illinois 

Pennsylvania 

Oregon 
Louisiana 

As  a  result  of  a  test  of  the  completeness  of  the  registra- 
tion of  deaths  in  Hawaii  the  territory  was  admitted  to  the 
registration  area  for  deaths  for  1917,  thus  extending  be- 
yond the  -Continental  United  States  the  area  from  which 
the  Bureau  of  the  Census  annually  collects  and  publishes 
mortality  statistics.  The  population  and  land  area  of 
Hawaii  are  not  included  in  the  figures  of  the  above  table. 

The  states  in  which  the  registration  of  deaths  is  still 
too  unsatisfactory  to  warrant  inclusion  in  the  registration 
area  are:  Alabama,  Arizona,  Arkansas,  Delaware,  Florida, 
Georgia,  Idaho,  Iowa,  Mississippi,  Nebraska,  Nevada, 
New  Mexico,  North  Dakota,  Oklahoma,  South  Dakota, 
Texas,  West  Virginia,  and  Wyoming.  (1918.) 


126 


ENUMERATION  AND   REGISTRATION 


*"    ^5> 


r 


«f 


* 


SS 


NEED  OF  NATIONAL  STATISTICS  127 

United  States  registration  area  for  births.  —  A  regis- 
tration area  for  births  was  not  established  until  1915.  For 
this  year  the  Bureau  of  the  Census  published  its  first  annual 
report  of  birth  statistics  based  on  registration  records.  The 
birth  statistics  published  in  connection  with  the  regular 
decennial  reports  from  1850  to  1900  inclusive  were  based 
on  enumerator's  returns. 

The  registration  area  in  1915  included  only  ten  states  — 
Maine,  New  Hampshire,  Vermont,  Massachusetts,  Rhode 
Island,  Connecticut,  New  York,  Pennsylvania,  Michigan, 
Minnesota,  and  the  District  of  Columbia.  In  these  states 
the  registration  of  births  is  believed  to  include  upwards 
of  ninety  per  cent  of  the  actual  numbers.  This  registration 
area  includes  only  10  per  cent  of  the  area  and  31  per  cent 
of  the  population  of  the  country.  In  spite  of  this  unfavor- 
able showing  a  beginning  has  been  made,  and  inasmuch  as 
the  standard  birth  certificate  has  been  adopted  for  85  per 
cent  of  the  population  and  as  public  sentiment  in  regard  to 
the  importance  of  vital  statistics  is  rapidly  gaining  ground, 
it  is  likely  that  the  registration  area  for  births  will  rapidly 
extend.  No  state  is  admitted  until  the  accuracy  of  its 
records  have  been  submitted  to  test. 

In  1916  Maryland  was  added.  In  1917,  Virginia, 
North  Carolina,  Kentucky,  Indiana,  Ohio,  Wisconsin, 
Washington,  Utah  and  Kansas  were  added,  bringing  the 
population  included  up  to  53.1  per  cent. 

Need  of  national  statistics.  —  More  and  more  it  becomes 
obvious  that  there  is  need  of  a  national  system  of  keeping 
records  of  vital  statistics,  with  uniform  state  laws,  and 
with  proper  provision  for  the  local  use  of  the  data  regis- 
tered. The  excellent  work  done  by  the  Bureau  of  the 
Census  has  done  much  to  emphasize  this  need.  Likewise 
interstate  barriers  must  be  broken  down  in  the  interest  of 
suppressing  diseases  dangerous  to  the  public  health.  The 


128  ENUMERATION  AND  REGISTRATION 

U.  S.  Public  Health  Service  keeps  a  record  of  cases  of 
diseases  from  data  furnished  by  the  states  and  publishes 
the  same  in  its  weekly  Public  Health  Reports.  This  is 
only  a  part  of  what  is  needed.  If  the  time  ever  comes 
when  the  United  States  establishes  a  real  National  Health 
Department  the  maintenance  of  an  adequate  system  of 
vital  records  will  be  one  of  supreme  importance. 

EXERCISES  AND    QUESTIONS 

1.  Compare  the  methods  of  numeration  used  in  taking  the  U.  S. 
census  of  1910,  with  those  used  in  1900,  1890,  1880,  etc. 

2.  How  do  these  methods  compare  with  those  used  in  England, 
France,  Sweden? 

3.  Would  there  be  any  advantage  in  making  the  census  date,  "as 
of  January  first "? 

;  4. "What  advantages  would  come  from  the  adoption  of  a  uniform 
census  date  for  the  entire  world? 

5.  How  accurately  is  the  population  of  China  known? 

6.  To  what  extent  is  the  keeping  of  accurate  census  records  and 
records  of  vital  statistics  an  index  of  national  progress? 

7.  How  can  improvements  be  made  in  ascertaining  the  facts  con- 
cerning morbidity? 


CHAPTER  V 
POPULATION 

Estimation  of  population.  —  It  is  only  for  the  census 
years  that  populations  can  be  known  with  certainty.  For 
the  intercensal  years,  the  years  between  two  censuses,  it 
is  necessary  to  depend  upon  estimates.  This  is  also  the 
case  for  the  postcensal  years,  namely,  the  years  following 
the  last  census.  These  estimates  are  only  approximately 
true,  a  fact  which  must  not  be  forgotten,  but  they  are 
sufficiently  near  the  truth  for  many  practical  uses. 

Estimations  of  population  may  be  made  in  various  ways. 
The  natural  growth  of  population  is  like  that  of  money  at 
compound  interest  except  that  the  interest  is  being  added 
constantly  instead  of  semi-annually  or  quarterly.  Mathe- 
maticians call  this  geometrical  progression.  With  a  given 
constant  rate  of  interest  money  in  the  bank  increases  more 
and  more  each  year.  It  is  the  same  with  population.  In 
geometrical  progression  the  basis  of  our  population  estimates 
is  the  annual  rate  of  increase.  When  dealing  with  very 
large  populations,  and  especially  when  dealing  with  popu- 
lations not  influenced  by  emigration  or  immigration,  this 
method  is  the  most  accurate  one  to  use.  It  has  several 
practical  disadvantages,  however,  and  in  the  present  shift- 
ing condition  of  the  world's  population  there  are  not  many 
places  where  the  natural  growth  of  population  is  the  only 
factor  to  be  considered. 

A  simpler  method  is  that  of  arithmetical  progression, 
which  assumes  a  constant  annual  increment  between  two 

129 


130  "  POPULATION 

census  years.  The  increase  in  ten  years  divided  by  ten  gives 
the  annual  increase.  This  is  practically  the  method  by  which 
money  increases  by  simple  interest.  The  arguments  in. 
favor  of  this  method  of  estimating  population  are  that  it  is 
simple  and  easily  understood;  that  in  view  of  the  various 
disturbing  factors  due  to  migration  and  other  causes  it  gives 
results  practically  as  near  the  truth  as  those  obtained  by 
geometrical  progression;  that  the  estimates  for  the  whole  area 
of  a  given  district  will  be  equal  to  the  sum  of  the  estimates 
for  all  the  parts  of  the  district,  which  would  not  be  the  case 
with  the  geometrical  method.  The  U.  S.  Bureau  of  the 
Census  has  adopted  this  method,  and  in  the  interest  of  uni- 
formity all  cities  and  states  should  do  the  same.  The 
method  is  one  which  should  not  be  extended  far  into  the 
future.  In  vital  statistics  it  is  not  necessary  to  extend  it 
beyond  ten  years  from  the  last  census,  for  ten  years  always 
brings  another  census. 

Another  method  is  that  of  using  local  data  as  indices  — 
such  as  the  number  of  registered  voters,  the  number  of  new 
building  permits,  the  number  of  school  children,  the  number 
of  names  in  the  directory,  the  bank  clearings,  the  number  of 
passengers  carried  by  the  trolley  cars,  etc.  These  facts  are 
often  obtainable  for  each  year  and  serve  as  valuable  checks 
on  the  census  method,  but  as  a  rule  they  should  not  be 
depended  upon  alone.  Common  sense  must  be  used.  What 
is  wanted  are  the  facts,  and  rigid  adherence  to  a  rule  when 
the  result  is  manifestly  unfair  is  absurd.  When  deviations 
from  accepted  practice  are  made,  however,  a  statement  of 
the  method  of  making  the  estimates  of  the  population 
should  always  accompany  the  result.  Even  the  U.  S.  Census 
utilizes  local  data  to  modify  its  estimates  where  plainly 
necessary., 

Estimates  of  population  might  be  made  from  records  of 
births  and  deaths  if  these  were  accurately  kept  and  if  the 


ADJUSTMENT  OF  POPULATION  TO  MID-YEAR     131 

migrations  of  the  people  were  known.  Practically  this 
method  is  useless. 

One  item  in  connection  with  the  estimation  of  the  popula- 
tion of  cities  should  not  be  lost  sight  of,  namely,  that  of 
changing  boundaries.  Cities  often  grow  by  extending  their 
area.  Increases  of  population  from  this  cause  should  not 
be  mistaken  for  natural  increase  in  population. 

Arithmetical  increase.  —  Let  us  assume  that  the  popu- 
lation of  a  place  in  1900  was  70,000  and  in  1910,  100,000. 
The  increase  was,  by  the  arithmetical  method,  30,000  in  ten 
years,  or  3000  in  each  year.  For  1904,  therefore,  the  esti- 
mated population  would  be  70,000  plus  four  times  3000  or 
82,000;  and  for  1915  it  would  be  100,000  plus  five  times 
3000  or  115,000.  It  is  assumed  that  within  the  ten  years 
following  the  last  census  the  annual  increase  will  be  the  same 
as  the  average  annual  increase  between  the  last  two  censuses. 
This  is  the  simple  and  customary  way  of  making  the  estimates. 

It  must  be  remembered  that  between  these  particular 
censuses  the  interval  was  not  exactly  ten  years.  The  census 
of  1900  was  "as  of  June  1st,"  that  of  1910  "as  of  April  15th." 
Consequently,  the  interval  was  ten  years  less  a  month  and 
a  half  or  9|  years  ( =  9.875  years).  The  average  increase  was 
not,  therefore,  3000  per  year,  but  30,000  -t-  9.875  or  3038. 
This  would  make  the  estimated  population  82,152  for  1904 
and  115,190  for  1915.  It  will  be  seen  that  this  difference 
is  not  great.  Nevertheless,  it  is  a  correction  which  in  some 
cases  is  of  importance.  Whether  it  will  have  to  be  made 
after  the  next  census  will  depend  upon  the  date  decided 
upon.  Strictly  speaking,  the  populations  of  the  census 
years  should  be  adjusted  to  the  middle  of  the  year  before 
the  average  annual  increments  are  computed. 

Adjustment  of  population  to  mid-year.  —  The  census  of 
1910  was  "as  of  April  15th."  What  then  was  the  population 
on  July  1st  ? 


132  POPULATION 

On  June  1,  1900,  the  population  was  70,000.  The  av- 
erage annual  increase  was  3038  per  year,  or  3038  -5-  12  = 
253  per  month.  On  July  1,  1900,  the  population  was, 
therefore,  70,000  +  253  =  70,253.  On  July  1,  1910,  it  was 
100,000  +  253  X  2 \  months  or  100,633.  The  increase  in 
ten  years  was,  therefore,  100,633  -  70,253  =  30,380,  or  3038 
per  year,  as  before. 

This  arithmetical  method,  therefore,  is  used  in  adjusting 
the  population  for  the  census  years  from  the  day  on  which 
the  census  was  actually  taken  to  the  mid-year. 

For  example,  on  June  1,  1900,  the  population  of  the  state 
of  Indiana  was  2,516,462;  on  Apr.  15,  1910,  it  was  2,700,876, 
an  increase  of  184,414  in  118.5  months.  On  July  1,  1910, 
i.e.,  2.5  months  later  than  the  census  date,  the  estimated 

population  would  therefore  be  2,700,876  +  -  ^  X  184,414 

Ilo.O 

or  2,704,767.  This  is  the  figure  used  by  the  U.  S.  Census  in 
the  Mortality  Report  of  that  year. 

Geometrical  increase.  —  A  simple  rule  for  computing 
populations  by  the  geometrical  method  is  to  use  the  loga- 
rithms of  the  populations  concerned  in  the  same  way  that 
the  populations  are  used  in  computing  by  the  arithmetical 
method.  Let  us  assume,  as  before,  that  the  population  was 
70,000  in  1900  and  100,000  in  1910.  The  logarithm  of 
100,000  is  5.0000,  that  of  70,000  is  4.8451.  Instead  of  sub- 
tracting 70,000  from  100,000  we  subtract  4.8451  from  5.0000 
and  get  0.1549.  Instead  of  dividing  30,000  by  10  we  divide 
0.1549  by  10  and  get  0.01549.  Then  we  multiply  this  by  4 
and  get  0.0620.  Finally,  we  add  this  to  4.8451,  which  is  the  log 
of  70,000,  and  get  4.9071.  This  is  the  log  of  the  answer,  which 
is  80,750.  The  following  comparison  ought  to  make  this  clear : 

Example.  —  The  population  of  a  city  in  1900  was  70,000 
and  in  1910,  100,000.  What  was  the  population  in  1904, 
in  1915  and  in  1925? 


FORMULA  FOR  GEOMETRICAL  INCREASE 


133 


TABLE  21 


Arithmet- 
ical method. 

Geometrical  method. 

(1) 

(2) 

(3) 

Population  in  1910.  . 
"   1900.. 
Increase  in  10  years- 
Increase  in  1    year. 

100,000 
70,000 

log  of  100,000  =  5  0000 
"    "     70,000  =  4.8451 

30,000 
3,000 

0.1549 
0.0155 

Increase  in  4  years.  . 

12,000 

0  0620 

Population  in  1900.  . 
"   1904.. 

70,000 
82,000 

4.8451 
log  of  80,750  =  4  9071 

Increase  in  5  years.  . 
Population  in  19fO.  . 
"   1915.. 

15,000 
100,000 
116,000 

0.0775 
5.0000 
log  of  119,500  =  5.  0775 

Increase  in  15  years. 
Population  in  1940.  . 
"    1925.. 

45,000 
100,000 
146,000 

0.2325 
5.0000 
log  of  170,800  =  5.2325 

It  will  be  noticed  that  for  intercensal  years  the  arithmet- 
ical method  gives  higher  estimates  than  the  geometrical, 
but  that  for  postcensal  years  the  geometrical  results  are 
higher.  This  is  illustrated  graphically  by  Fig.  30. 

Formula  for  geometrical  increase.  —  The  mathematical 
formula  for  geometrical  increase  is 

Pn  =  PC  (1  +  rj», 

in  which  Pc  is  the  population  at  one  census,  Pn  is  the 
population  n  years  after  Pc,  r  is  the  annual  rate  of  increase 
and  n  is  the  number  of  years. 

Let  us  apply  this  to  the  case  already  considered.  Here 
we  know  the  two  populations  Pe  and  Pn,  70,000  and  100,000, 


134 


POPULATION 


180 


170 


160 


150 


140 


130 


120 


110 


100 


90 


80 


70 


60 


-80,750 


Census 


170,800- 


119,500> 


//Ml5,000 


XT!f>nsi 


Census 


1900 


1910 


1920  1930 

FIG.  30.  —  Example  of  Arithmetical  and  Geometrical  Methods 
of  Estimating  Population. 


FORMULA  FOR  GEOMETRICAL  INCREASE          135 

and  we  know  that  n  is  10  years;  first  we  need  to  find  r, 
the  annual  rate  of  increase.  According  to  algebra  we  may 
rewrite  the  above  formula,  thus: 

log  Pn  -  log  PC  =  n  log  (1  +  r). 

Substituting  the  values  of  the  logarithms  of  100,000  and 
70,000  and  the  value  of  n  we  have 

5.0000  -  4.8451  =  10  log  (1  +  r) 

0.1549  =  10  log  (1  +  r) 

0.01549  =       log  (1  +  r) 

and  from  the  tables  of  logarithms  (1  -f  r)  is  found  to  be 
1.036,  hence  r  =  1.036  -  1  =  0.036,  or  3.6  per  cent.  There- 
fore, the  average  annual  rate  of  increase  between  1900  and 
1910  was  3.6  per  cent. 

Knowing  this  rate  and  assuming  it  to  be  constant  we  can 
find  the  population  in  any  other  year.  Suppose  we  try 
1925,  15  years  after  1910.  Then  we  have: 

Pn  =  100,000  (1  +  0.036)15, 
log  Pn  =  log  100,000  +  15  log  1.036 

=  5.0000  +  15  X  0.01549, 
log  Pn  =  5.23245, 
/.     Pn  =  17,079  (according  to  the  log.  tables.) 

By  the  use  of  this  formula  many  interesting  problems  can 
be  solved.  For  example,  how  many  years  would  it  take  the 
population  in  our  now  familiar  example  to  reach  200,000? 
We  know  that  the  average  rate  of  increase  between  1900  and 
1910  was  3.6  per  cent.  Therefore,  we  have  in  the  formula 

200,000  =  100,000  (1  +  0.036)n. 
We  want  to  find  the  value  of  n.     We  have 

log  2000,00  =  log  100,000  +  n  log  1.036, 
5.30103  =  5.0000  +  n  X  0.01549, 
0.30103  =  rt  X  0.01549, 

0.30103  _ 

^  =  001549  =  19'4 


136  POPULATION 

Strictly  speaking,  we  have  no  reason  to  use  a  year  or  even 
a  month  -as  the  basis  of  compounding,  as  the  population  is 
increasing  from  day  to  day  and  from  hour  to  hour.  A  more 
accurate  formula  may  be  found  in  books  on  calculus.  We 
do  not  need  to  use  it  in  this  work. 

Rate  of  increase.  —  The  population  of  the  United  States 
on  June  10,  1900,  was  75,994,575;  on  Apr.  15,  1910,  it  was 
91,972,266.  The  increase  in  9J  years  was  15,977,691  or, 
134,833  per  month,  assuming  the  increase  to  have  been 
constant.  We  might  divide  this  still  further  and  say  that 
the  average  increase  was  4494  per  day,  or  about  3.12  persons 
per  minute.  On  this  basis  we  might  also  by  computation 
ascertain  that  the  population  of  the  United  States  passed  the 
one  hundred  million  mark  at  4  o'clock  on  Apr.  3,  1915. 
Such  statements  as  this  have  a  fascination  for  certain  people, 
but  they  are  of  idle  moment.  They  merely  serve  to  illustrate 
the  method  of  computation  by  the  arithmetical  method. 
Had  the  geometrical  method  been  used  the  result  would  have 
been  different.  As  a  matter  of  fact  no  one  will  ever  know 
just  when  the  population  passed  the  hundred  million  mark. 

If  we  take  the  above  figures  for  1900  and  1910  and  regard 
them  as  representing  a  ten  year  period  (instead  of  9.875 

15,977,691 
years),  the  increase  amounts  to  ,.,  ftfM  ,,_,  or  21  per  cent. 


We  may  divide  this  by  10  and  say  the  annual  increment  was 
2.1  per  cent,  or  more  accurately  by  9.875  and  say  that  it  was 
2.13.  But  we  ought  not  to  use  the  word  rate  in  this  connec- 
tion. As  a  matter  of  fact,  if  the  rate  of  increase  in  10  years 
was  21  per  cent,  the  average  annual  rate  would  not  be  2.1 
per  cent.  If  in  the  formula  for  geometrical  increase  we  let 
Pc  =  100  and  Pn  =  121,  which  would  represent  an  increase 
of  21  per  cent  in  10  years,  then 

log  121   -  log  100  =  10  log  (1  +  r), 
2.08278  -  2.00000  =  10  log  (1  +  r), 


DIFFERENCE  BETWEEN  ESTIMATE  AND  FACT      137 


from  which 


r  =  1.92  per  cent,  not  2.1  per  cent. 


This  assumes  that,  as  we  might  say,  the  interest  is  com- 
pounded annually. 

This  error  of  dividing  the  percentage  increase  in  10  years 
by  10  to  find  the  annual  increase  is  sometimes  made  in  using 
the  geometrical  method  of  estimating  increase.  Obviously 
with  compound  interest  a  lower  rate  suffices  to  produce  a 
given  increase  in  10  years  than  with  simple  interest.  The 
proper  way  to  find  the  annual  rate  is  by  the  use  of  the 
formula. 

Decreasing  rate  of  growth.  —  It  seems  to  be  generally 
true  that  as  cities  become  larger  their  annual  rate  of  growth 
decreases.  A  study  of  six  American  cities  gave  the  following 
annual  rates  of  increase  when  the  populations  were  as 
indicated. 

TABLE  22 
DECREASING  RATE  OF  GROWTH  OF  CITIES 


Stage  of 
Population 

Annual  percent- 
age Increase. 

(1) 

(2) 

100,000 

4.85 

200,000 

3.59 

300,000 

2.91 

400,000 

2.48 

500,000 

2.02 

600,000 

1.75 

700,000 

1.66 

800,000 

1.58 

Difference  between  estimate  and  fact.  —  In  estimating 
the  population  either  by  the  arithmetical  or  geometrical 
method  we  are  assuming  something  which  is  almost  never 
true,  i.e.,  that  the  population  is  increasing  regularly.  As  a 


138  POPULATION 

matter  of  fact  the  increase  is  not  regular  from  year  to  year. 
Therefore,  any  estimate  may  be  erroneous.  In  the  absence 
of  the  facts,  however,  we  are  compelled  to  resort  to  the 
method  of  estimation.  Also  when  we  assume  that  the  growth 
in  the  present  decade  is  the  same  as  in  the  last  decade  we 
assume  a  uniformity  of  conditions  which  seldom  obtains. 
Let  us  check  a  few  of  our  estimates  by  actual  census  returns. 

In  Cambridge,  Mass.,  the  census  population  was  70,028 
in  1890  and  91,886  in  1900,  a  gain  of  21,858  in  the  decade. 
If  the  same  increase  had  continued  during  the  next  decade 
the  population  would  have  been  113,744.  The  census  of 
1910  was,  however,  only  104,839. 

In  Detroit,  Michigan,  the  population  in  1890  was  205,876 
in  1900  it  was  287,704,  the  increase  being  79,828.  If  this 
increment  continued  regularly  the  population  in  1910  would 
have  been  365,532;  actually  it  was  465,766.  This  of  course 
is  an  extreme  case.  In  most  cities  the  estimates  agree  fairly 
well  with  the  facts. 

Let  us  take  the  case  of  a  larger  population,  say  that  of  the 
United  States.  In  1890  the  population  was  62,947,714,  in 
1900,  75,994,575,  the  decadal  increase,  1,304,861.  The  esti- 
mate for  1910  based  on  these  figures  would  have  been 
89,041,436  by  arithmetrical,  or  91,723,000  by  geometrical 
increase.  Actually  the  population  in  1910  was  91,972,266. 
For  large  populations  like  this  the  geometrical  method  gives 
closer  results. 

Revised  estimates.  —  Suppose,  however,  that  as  in 
Cambridge,  Mass.,  the  census  of  1910  showed  that  the  city 
had  not  grown  as  fast  as  in  the  decade  from  1890  to  1900, 
what  shall  be  done  with  the  estimates  already  made  for  the 
years  1901  to  1909,  inclusive?  Obviously  they  were  not 
correct  even  on  the  theory  of  steady  increase.  Yet  they 
have  been  used  as  the  basis  of  computing  birth-rates  and 
death-rates.  The  answer  is  that  if  the  discrepancy  is  large 


POPULATION  FROM  ACCESSIONS  AND  LOSSES       139 


the  populations  for  those  years  should  be  reestimated  and 
the  birth-rates  and  death-rates  recomputed.  Let  us  see 
what  differences  would  result. 

TABLE  23 
REVISION  OF  POPULATION  ESTIMATES 


Year. 

Census. 

Postcensal  estimate 
based  cm  1890-1900. 

Intercensal  estimate 
'  based  on  1900-1910. 

(1) 

(2) 

(3) 

(4) 

1890 

70,028 

1900 

91,886 

1 

94,072 

93,181 

2 

96,258 

94,476 

3 

98,444 

95,771 

4 

100,630 

97,066 

5 

102,816 

98,361 

6 

105,002 

99,656 

7 

107,188 

100,951 

8    1 

109,374 

102,246 

9 

111,560 

103,541 

10 

104,839 

Ordinarily  the  errors  are  not  as  great  as  this  and  no 
correction  need  be  made,  but  the  chance  of  error  is  so  great 
that  old  published  figures  for  death-rates  should  not  be 
accepted  at  their  face  value  until  the  population  estimates 
have  been  carefully  examined  for  errors  of  this  sort. 

It  would  be  sound  practice  to  revise  all  rates  based  on 
postcensal  population  estimates  every  ten  years,  i.e.,  after 
each  new  census. 

Estimation  of  population  from  accessions  and  losses.  — 
In  a  place  where  records  of  the  births  and  deaths  are  accu- 
rately kept  it  would  be  possible  to  use  them  in  estimating 
population,  but  emigration  and  immigration  enter  as  dis- 
turbing factors.  Two  examples  of  this  method  will  illustrate 
the  way  in  which  this  method  works  out. 


140  POPULATION 

In  England  and  Wales  the  data  were  as  follows: 

Population  in  1891 29,000,000 

Births,  1891  to  1901 9,160,000 

38,160,000 
Deaths,  1891  to  1901 5,560,000 

Computed  population  in  1901 32,600,000 

Census  gave,  for  the  year  1901 32,530,000 

Difference  representing  excess  of  emigration  over 

immigration 70,000 

In  Massachusetts  the  population  for  1910  computed  in 
this  way  was  3,092,349,  but  the  census  gave  3,366,416,  an 
excess  of  274,067,  which  represented  in  part  the  excess  of 
immigration  over  emigration  and  in  part,  no  doubt,  incom- 
plete registration  of  births. 

Estimation  of  future  population.  —  For  some  purposes, 
as,  for  example,  in  planning  for  sewerage  or  water  supply 
systems,  it  is  necessary  to  estimate  the  population  of  a  city 
for  half  a  century  or  more  in  the  future.  This  cannot  be 
safely  done  by  mathematical  methods  alone,  for  much  depends 
upon  other  things  not  subject  to  definite  analysis.  Bound- 
aries may  change,  business  and  manufacturing  may  expand 
or  contract  in  ways  unforeseen,  changes  in  transportation  or 
in  methods  of  housing  may  influence  the  problem.  Mathe- 
matical analyses  are  helpful,  but  the  conclusions  must  be 
tempered  with  judgment  based  on  a  study  of  local  conditions 
and  on  the  history  of  other  cities  similar  in  size  and  conditions. 

A  few  examples  of  unfulfilled  estimates  may  be  mentioned. 
In  1865  Jas.  P.  Kirkwood,  a  well  known  civil  engineer, 
estimated  that  the  population  of  Cincinnati  would  be 
431,644  in  1890;  actually  it  proved  to  be  297,000. 

At  Rochester  an  estimate  made  in  1889  claimed  that  the 
population  in  1910  would  be  283,459;  actually  this  city  grew 
to  218,149.  At  Winnipeg  in  1897  a  certain  estimate  of  the 


GRAPHICAL  METHOD  OF  ESTIMATING  POPULATION     141 

probable  population  in  1907  was  made,  but  when  1907 
arrived  the  population  was  double  the  estimated  figure. 

For  long-time  estimates  the  methods  already  described 
may  be  used,  but  with  this  difference  that  the  rate  of  past 
increase  is  best  obtained,  not  by  taking  the  results  of  the 
last  two  censuses  only,  but  by  considering  a  longer  period. 
To  look  farther  ahead  than  10  years  you  must  begin  farther 
back.  This  is  an  'important  ppinciple  which  applies  to  many 
things  in  life.  It  means  the  use  of  experience.  The  public 
health  student  who  desires  to  project  himself  forcefully  into 
the  coming  era  needs  to  study  the  past  history  of  the  health 
of  the  human  race.  It  is  equally  true  in  the  fields  of  science, 
philosophy  and  religion. 

As  a  rule  in  United  States  cities  the  arithmetical  method 
gives  "results  which  are  too  low,  and  the  geometrical  method 
gives  results  which  are  too  high.  All  things  considered  the 
graphical  method  is  the  most  serviceable  for  long  term  esti- 
mates as  it  enables  data  for  various  cities  to  be  brought 
together. 

Immigration.  —  The  irregular  effect  of  immigration  in 
the  United  States  may  be  inferred  from  Fig.  31,  which 
shows  the  immigration  by  years  from  1820  to  1909.  Immi- 
gration has  occurred  in  a  series  of  waves,  resulting  from  the 
relative  economic  conditions  in  this  country  and  abroad. 
When  this  incoming  population  has  been  concentrated  in 
manufacturing  cities,  as  has  periodically  been  the  case,  it  has 
been  followed  by  an  increased  prevalence  of  disease.  The 
subject  is,  therefore,  an  important  one  for  sanitarians  to 
consider. 

The  data  for  immigration  are  published  in  the  annual 
reports  of  the  U.  S.  Commissioner  General  of  Immigration. 

Graphical  method  of  estimating  population.  —  The  simp- 
lest method  of  estimating  future  populations  graphically  is 
to  plot  the  populations  on  cross-section  paper  using  all  past 


142 


POPULATION 


records  available,  and  then  sweep  the  curve  forward  accord- 
ing to  its  general  trend.  It  is  easy  to  use  poor  judgment  in 
doing  this.  Local  conditions  should  be  kept  in  mind  and 
especially  additions  of  area  should  be  considered. 


1,300,000 


100,000 


1820   1830   1840   1850   1860   1870   1880   1890   1900   1910   1920 

FIG.  31.  —  Immigration  to  the  United  States:  1820-1917.     (From 
report  of  Commissipner  of  Immigration.) 

A  safer  way  is  to  plot  not  only  the  populations  for  the  city 
being  considered,  but  for  other  cities  where  the  conditions 
are  near  enough  to  warrant  them  being  taken  as  guides. 


GRAPHICAL  METHOD  OF  ESTIMATING  POPULATION     143 

These  cities  must  be  larger  than  the  one  for  which  the  esti- 
mate is  to  be  made. 

A  good  way  is  to  plot  them  all  on  cross-section  paper  on 
the  same  scale  and  then  trace  the  lines  upon  a  single  sheet, 
adjusting  the  time  scale  so  that  all  of  the  curves  meet  and 
cross  on  some  selected  year,  usually  the  last  census  year.  In 
this  way  there  will  be  a  number  of  population  lines  extending 
ahead  and  these  may  be  used  as  guides  in  sweeping  in  the 
curve  of  the  city  being  considered. 

Judgment  inevitably  plays  a  large  part  in  long-term  esti- 
mates and  statistics  are  used  merely  as  an  aid  to  that 
judgment. 

Example.  —  Estimate  the  future  population  of  Springfield, 
Mass.,  using  for  comparison  the  cities  of  Worcester,  Mass., 
Syracuse,  N.  Y.,  Rochester,  N.  Y.,  and  Providence,  R.  I. 
From  the  census  reports  we  have  the  following  data: 


TABLE  24 
POPULATION  6F  CITIES 


Year. 

Springfield. 

Worcester. 

Syracuse. 

Rochester. 

Providence. 

(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

1860 

15,199 

24,960 

28,119 

48,204 

50,666 

1870 

26,703 

41,105 

43,051 

62,386 

68,904 

1880 

33,340 

58,291 

51,792 

89,366 

104,857 

1890 

44,179 

84,655 

88,143 

133,896 

132,146 

1900 

62,059 

118,421 

108,374 

162,608 

175,597 

1910 

88,926 

145,986 

137,249 

218,149 

224,326 

These  data  are  first  plotted  as  in  the  upper  part  of  Fig.  32. 
They  are  afterwards  brought  together  as  in  the  lower  part  of 
the  figure,  the  lines  being  made  to  cross  on  the  line  of  1910. 
The  estimate  for  Springfield  is  made  by  sweeping  the  curve 
forward  as  shown. 


144 


POPULATION 


200,000 


o  150,000 
| 

f 


FIG.  32.  —  Example  of  Graphical  Method  of  Estimating  Future 
Population. 


ACCURACY  OF  STATE  CENSUSES  145 

Accuracy  of  state  censuses.  —  The  U.  S.  Bureau  of  the 
Census  does  not  recognize  as  generally  acceptable  the  results 
obtained  by  those  states  which  enumerate  their  populations 
in  the  years  which  end  in  5,  on  the  ground  that  it  does  not 
control  such  intermediate  censuses  and  has  no  way  of  assur- 
ing itself  of  their  accuracy.  On  the  whole  this  position  is 
probably  sound.  In  Massachusetts,  the  last  federal  census 
in  1910  was  made  by  the  same  state  authority,  namely  the 
Director  of  the  Massachusetts  Bureau  of  Statistics,  which 
has  made  the  state  census,  and  one  census  is  presumably  as 
accurate  as  the  other. 

In  the  past,  however,  the  state  censuses  have  evidently 
not  been  as  accurate  as  the  federal  censuses.  If  the  results 
of  the  federal  censuses  for  Massachusetts  are  plotted  the 
points  fall  on  quite  a  smooth  and  regular  curve  from  1820  to 
1910,  the  only  important  departure  being  during  the  decade 
of  the  Civil  War.  The  figures  for  the  state  censuses  do  not 
all  fall  on  this  line,  but  rise  and  fall  irregularly.  This  is 
presumptive,  though  not  conclusive,  proof  of  the  inaccuracy 
of  some  of  the  figures  (Fig.  33). 

The  Massachusetts  state  census  was  taken  on  May  1 
from  1855  to  1905,  inclusive;  in  1915  it  was  taken  on 
April  1. 

The  question  often  comes  up  for  decision,  shall  the  state 
censuses  be  used  in  estimating  populations  for  the  years  in  the 
last  half  of  each  decade  ?  For  the  sake  of  uniformity  it  is  best 
to  use  the  federal  figures  only.  But  these  figures  should,  of 
course,  be  modified  if  the  state  census  reveals  that  there 
have  been  important  changes  in  conditions.  The  state 
figures  should  be  used,  therefore,  as  a  check  on  the  estimates 
based  on  the  federal  results.  Should  glaring  differences  be 
noticed  their  cause  should  be  investigated.  If  state  figures 
are  used  this  fact  should  be  stated  in  connection  with  the 
estimate. 


146 


POPULATION 


Urban  and  rural  population.  —  It  is  common  to  classify 
the  population  of  a  country  into  " urban "  and  "rural." 
This  is  done  for  purposes  of  discussion,  the  idea  being  to 
separate  the  people  living  in  sparsely  settled  regions  and 
small  villages  from  those  living  in  cities,  on  the  theory  that 

4,000, 000 


3,000,000 


1 2,000, 000 

I 


1,000,000 


/ 

/ 

/ 

/ 

/ 

/ 

. 

/ 

y 

/ 

/^ 

,-f 

-'A 

x 

^ 

;> 

/" 

\s 

^ 

^ 

*-*• 

^-" 

• 

Fe 

Uor. 

U  C 

U81 

• 

0 

Stt 

itc 

3011 

HIS 

1830    1840     1850     1860 


1890     1900     1910 


1870     1880 
Years 

FIG.  33.  —  Population  of  Massachusetts  according  to  Federal  and 
State  Censuses.     (The  effect  of  the  Civil  War  should  be  noticed.) 

the  former  lead  a  more  individualistic  life,  while  the  latter 
lead  a  more  communal  life.  In  cities  for  example,  water 
supplies,  sewerage  systems,  food  supplies,  methods  of  trans- 
portation and  various  public  utilities  are  used  in  common  by 
all,  while  in  the  country  each  household  has  its  own  well,  its 
own  garden,  its  own  cesspool,  its  own  means  of  transporta- 
tion. Thus  urban  and  rural  populations  are  supposed  to 
live  and  work  under  different  conditions. 


URBAN  AND  RURAL  POPULATION  147 

Obviously  the  separation  of  the  -two  classes  must  be  an 
arbitrary  one.  In  the  United  States  prior  to  the  Census  of 
1880  the  limit  of  8000  inhabitants  was  used.  In  1880  it 
becamejecognized  that  many  communities  of  less  than  8000 
inhabitants  possessed  "the  distinctive  features  of  urban 
life,"  and  accordingly  the  limit  was  dropped  to  4000,  although 
the  old  limit  was  used  in  many  of  the  tabulations  of  the 
census  of  that  year,  and  also  of  the  years  1890  and  1900.  In 
1900  some  comparisons  of  the  two  limits  were  made.  It  was 
found,  for  example,  that  32.9  per  cent  of  the  population  of 
the  United  States  would  be  classed  as  urban  on  the  basis  of 
the  8000  limit,  and  37.3  per  cent,  on  the  basis  of  the  4000 
limit. 

In  1910  the  limit  was  reduced  by  the  Census  Bureau  to 
2500.  The  reason  for  this  probably  lay  in  the  extension  of 
various  public  utilities,  once  existing  only  in  the  cities  of 
larger  size,  to  the  smaller  communities.  In  1910,  46.3  per 
cent  of  the  population  were  classed  as  urban  on  the  basis  of 
the  2500  limit,  but  only  38.8  were  in  cities  larger  than 
8000. 

One  must  be  careful  in  drawing  conclusions  from  "urban 
and  rural  statistics."  In  the  first  place,  of  necessity  they 
relate  to  civil  divisions.  "Outside  of  New  England,"  says 
the  Census  Report  for  1900,  "there  is  not  much  difficulty  in 
distinguishing  between  the  urban  and  rural  elements  of  the 
population,  as  only  dense  bodies  of  population  are  chartered. 
But  in  New  England  a  town,  which  is  the  usual  division  of 
the  county,  is  chartered  bodily  as  a  city  when  certain  con- 
ditions of  population  are  fulfilled,  so  that  a  city  may  contain 
a  considerable  proportion  of  rural  population,  and,  conversely, 
a  town  may  contain  a  compact  body  of  population  of  magni- 
tude sufficient  to  be  classed  as  urban."  Evidently  then, 
rural  population  does  not  necessarily  mean  people  living  in 
isolation,  as  on  a  farm.  Almost  every  incorporated  town  or 


148  POPULATION 

borough  has  some  center,  and  here  people  may  live  under 
communal  conditions  which  may  be  quite  as  insanitary  as 
those  found  in  cities,  with  houses  close  together,  with  board- 
ing houses,  saloons,  stables,  numerous  cesspools,  and  even 
sewers  and  public  water  supplies. 

Attempts  have  been  made  by  various  writers  to  make  a 
triple  separation  of  the  population  into  "rural,"  "village," 
and  "urban,"  using  populations  of  1000  and  4000  as  de- 
markations.  These  add  but  little  to  the  value  of  the  statis- 
tics and  usually  it  is  best  to  follow  the  practice  of  the  Bureau 
of  the  Census.  Populations  of  3000  and  5000  have  also  been 
used  as  limits  between  rural  and  urban.  Whatever  limits 
are  used  the  possible  fallacies  inherent  in  an  arbitrary  classi- 
fication should  be  kept  in  mind. 

In  comparing  conditions  as  shown  by  censuses  ten  years 
apart  there  is  always  likely  to  be  some  confusion  caused  by 
communities  which  have  populations  near  the  limit  changing 
from  one  side  to  the  other.  The  Bureau  of  the  Census  nas 
followed  this  practice:  ''In  order  to  contrast  the  proportion 
of  the  total  population  living  in  urban  or  rural  territory  the 
territory  is  classified  according  to  the  conditions  as  they 
existed  at  each  census;  but  in  order  to  contrast  between  the 
rate  of  growth  of  urban  and  rural  communities  it  is  necessary 
to  consider  the  changes  of  population  for  the  same  territory, 
which  have  occurred  between  censuses,  and  the  places  in- 
cluded in  the  urban  class  are  those  which  have  populations 
above  the  limit  at  the  last  census,  even  though  they  were 
below  the  limit  at  the  time  of  the  previous  census. 

Since  about  1820  the  urban  population  of  the  country  has 
been  rapidly  increasing,  the  rural  population  becoming 
relatively  less.  This  is  well  shown  by  the  following 
figures: 


URBAN  AND  RURAL  POPULATION 


149 


TABLE  25 

TOTAL  AND  URBAN  POPULATION  AT  EACH  CENSUS: 
1790-1910 

(From  U.  S.  Census,  1900,  Vol.  1,  Pt.  1,  p.  LXXXIII.) 


Per  cent  of 

Census 
year. 

Total  population. 

Urban  population.  * 

Number  of 
places. 

urban  of 
total  popu- 
lation. 

(1) 

(2) 

(3) 

(4) 

(5) 

1790 

3,929,214 

131,472 

6 

3.3 

1800 

5,308,483 

210,873 

6 

4.0 

1810 

7,239,881 

356,920 

11 

4.9 

1820 

9,638,453 

475,135 

13 

4.9 

1830 

12,866,020 

864,509 

26 

6.7 

1840 

17,069,453 

1,453,994 

44 

8.5 

1850 

23,191,876 

2,897,586 

85 

12.5 

1860 

31,443,321 

5,072,256 

141 

16.1 

1870 

38,558,371 

8,071,875 

226 

20.9 

1880 

50,155,783 

11,450,894 

291 

22.8 

1890 

62,947,714 

18,327,987 

449 

29.1 

1900 

75,994,575 

25,142,978 

556 

33.1 

1910 

91,972,266 

35,726,720 

778 

38.8 

*  Population  of  places  of  8000  or  more  at  each  census. 

This  is  also  shown  by  the  increase  in  the  number  of  large 
cities  since  I860. 

TABLE  26 

TABLE  SHOWING  THE  INCREASE  IN  NUMBER    OF    LARGE 
CITIES  IN  THE  UNITED  STATES  BETWEEN  1860  AND  1910 


Number  of 

cities  with 
population 

I860. 

1870. 

1880. 

1890. 

1900. 

1910. 

above. 

(1) 

(2) 

(3) 

(4) 

(5)     • 

(6) 

(7) 

25,000 

32 

50 

77 

125 

161 

229 

50,000 

15 

24 

35 

58 

79 

109 

100,000 

8 

13 

20 

28 

38 

50 

500,000 

2 

2 

4 

4 

6 

8 

1,000,000 

0 

0 

1 

3 

3 

3 

150  POPULATION 

Density  of  population.  —  By  the  density  of  population 
we  usually  mean  the  number  of  persons  dwelling  upon  a  unit 
area  of  land,  as  a  square  mile  or  an  acre.  It  is  not  to  be 
supposed  that  the  persons  within  this  unit  area  are  uniformly 
distributed  over  it.  Usually  they  are  not.  The  ratio  is  one 
of  convenience,  however,  and  variations  of  density  within 
the  area  under  consideration  are  tacitly  assumed.  On  the 
catchment  area  of  the  Croton  river  (331  square  miles)  which 
supplied  New  York  with  unfiltered  water  the  population  in 
1903  was  on  an  average  about  52  per  square  mile,  while  on 
the  catchment  areas  of  many  German  streams,  where  the 
water  is  filtered  before  being  used  the  population  per  square 
mile  is  often  500  or  800.  Thus  the  average  density  expressed 
in  this  way  is  a  valuable  means  of  comparing  the  relative 
liability  of  the  water  to  be  contaminated,  even  though  both 
in  Germany  and  on  the  Croton  catchment  area  the  popula- 
tion consists  of  villages  and  farms  irregularly  scattered. 

The  average  density  of  the  population  of  the  United 
States  is  steadily  increasing.  In  1790  it  was  only  4.5  persons 
per  square  mile;  in  1860  it  was  10.6;  in  1910  it  was  30.9. 
The  density  varies  greatly  in  the  different  states.  Rhode 
Island  has  the  greatest  density.  In  1910  it  was  508.5  per 
square  mile,  Massachusetts  came  next  with  418.8,  then  New 
Jersey  with  337.7,  Connecticut,  231.3,  New  York,  191.2, 
Pennsylvania,  171,  Maryland,  130.3,  Ohio,  117,  Delaware, 
103,  and  Illinois,  100.6.  These  were  the  only  states  above 
100  per  square  mile.  In  Nevada  the  density  was  only  0.7 
per  square  mile. 

The  density  of  population  of  the  United  States  by  counties 
is  shown  in  Fig.  34. 

When  we  need  to  know  the  variations  in  density  more 
accurately  we  take  a  smaller  unit  of  area.  For  the  purpose 
of  calculating  the  size  of  sewers  required  in  a  district,  or  for 
studying  the  congestion  of  population  in  a  city  the  density 


DENSITY  OF  POPULATION 


151 


152 


POPULATION 


per  acre  is  computed.  The  population  density  in  cities 
usually  increases  with  their  population.  In  the  congested, 
portions  of  cities  the  density  may  be  several  hundred  per 
acre,  sometimes  over  a  thousand.  Fig.  35  shows  the  den- 
sities of  population  in  the  different  wards  of  Boston  and 
Cambridge  in  the  year  1910. 

There  are  two  ways  in  which  the  density  of  population 
of  a  city  may  be  computed.     The  first  and  most  com- 


200 


100,000      200,000       300,000       400,000 
Population 


500,000       600,000 


FIG.  35.  —  Density  of  Population  by  Wards  in  Boston  and  Cam- 
bridge, Mass.:  1910. 

mon  way  is  to  divide  the  population  by  the  area  in 
acres.  This  gives  the  actual  density  per  acre.  In  Boston, 
for  example,  in  1910  the  population  was  686,092,  the 
acreage  27,674,  and  the  number  of  persons  on  the 
average  acre  was  24.8.  But  if  we  look  at  the  density 
from  the  standpoint  of  the  people  we  find  that  the 
median  person  lives  where  the  density  is  about  50  per 
acre  and  that  10  per  cent  of  the  population  live  where  the 
density  is  125  per  acre,  5  per  cent  where  it  is  150.  In 


POPULATION  OF  UNITED  STATES  CITIES         153 

Cambridge,  Mass.,  the  average  density  per  acre  is  25.1,  or 
practically  the  same  as  in  Boston.  The  density  for  the 
median  person  is  also  about  the  same,  i.e.,  50  per  acre;  but 
10  per  cent  of  the  population  live  where  it  is  less  than  60 
per  acre,  and  5  per  cent  where  it  is  only  100.  In  no  ward 
of  Cambridge  is  the  density  as  great  as  in  five  large  pop- 
ulous wards  of  Boston. 

For  some  purposes,  as  when  we  are  providing  a  sewerage 
system,  the  density  per  acre  is  what  is  wanted,  but  when 
we  are  considering  the  crowded  condition  of  the  people  it 
is  the  median  density  based  on  population  which  is  needed, 
and  the  proportion  of  people  living  under  conditions  of 
different  congestion.  We  need  also  to  consider  areas  as 
small  as  single  blocks. 

Population  of  United  States  Cities.  — The  figures  in 
Table  27  will  be  found  useful  in  computing  vital  rates.  They 
are  based  on  published  reports  of  the  U.  S.  Bureau  of  the 
Census. 


154 


POPULATION 


TABLE  27 

POPULATION   OF  UNITED  STATES  CITIES  HAVING,  IN 
1910,  25,000  INHABITANTS  OR  MORE 


1900. 

1910. 

1916  (estimate). 

(1) 

(2) 

(3) 

(4) 

Alabama 
Birmingham  
-  Mobile  

38,415 
38,469 

132,685 
51,521 

181,762 
58,221 

Montgomery 

30,346 

38,136 

43,285 

Arkansas 
Little  Rock 

38,307 

45,941 

57,343 

California 
Berkeley     .  .           

13,214 

40,434 

57,653 

Los  Angeles       

102,479 

•  319,198 

503,812 

Oakland                 

66,960 

150,174 

198,604 

Pasadena  

9,117 

30,291 

46,450 

Sacramento  
San  Diego  

29,282 
17,700 

44,696 
39,578 

66,895 
53,330 

San  Francisco 

342,782 

416,912 

463,516 

San  Jose 

21,500 

28,946 

38,902 

Colorado                       

Colorado  Springs  
Denver  
Pueblo  

21,085 
133,859 

28,157 

29,078 
213,381 
44,395 

32,971 
260,800 
54,462 

Connecticut 
Bridgeport 

70,996 

102054 

121,579 

Hartford   ...    .        

79,850 

98  915' 

110,900 

Meriden  (town)  
Meriden  (city)  
New  Britain  

28,695 
24,296 
25,998 

32,066 
27,265 
43,916 

34,183 
29,130 
53,794 

New  Haven  

108,027 

133,605 

149,685 

Norwich  (town)  
Stamford  (town) 

24,637 
18,839 

28,219 
28,836 

29,419 
35,119 

Stamford  (city)  

15,997 

25,138 

30,884 

Waterbury  .-  

45,859 

73,141 

86,973 

Delaware 
Wilmington  

76,508 

87,411 

94,265 

District  of  Columbia 
Washington                 

278,718 

331,069 

363,980 

Florida 
Jacksonville  

28,429 

57,699 

76,101 

Tampa  .  .  

15,839 

37,782 

53,886 

Georgia 
Atlanta 

89,872 

154,839 

190,558 

Augusta                   

39,441 

41,040 

50,245 

POPULATION  OF  UNITED  STATES  CITIES         155 


TABLE  27 

POPULATION  OF  UNITED  STATES  CITIES  HAVING,  IN 
1910,  25,000  INHABITANTS  OR  MORE—  (Continued) 


1900. 

1910. 

1916  (estimate). 

(1) 

(2) 

(3) 

(4> 

Georgia  —  (Continued) 
Macon  

23,272 

40,665 

45,757 

Savannah  

54,244 

65,064 

68,805 

Illinois 
Aurora 

24,147 

29,807 

34,204 

Bloomington 

23,286 

25,768 

27258 

Chicago   .  . 

1,698,575 

2,185,283 

2,497,722 

Danville  ...       .     ... 

16,354 

27,871 

32,261 

Decatur  

20,754 

31,140 

39,631 

East  St.  Louis  

29,655 

58,547 

74,708 

Elgin.. 

22,433 

25,976 

28,203 

Joliet 

29353 

34670 

38010 

Peoria 

56  100 

66950 

71  458 

Quincy 

36252 

36587 

36  798 

Rockford 

31  051 

45,401 

55  185 

Springfield  

34,159 

51,678 

61,120 

Indiana 
Evansville                 

59,077 

69,647 

76,078 

Fort  Wayne  • 

45,115 

63,933 

76,183 

Indianapolis 

169,164 

233,650 

271,708 

South  Bend 

35,999 

53,684 

68,946 

Terre  Haute 

36,673 

58,157 

66,093 

Iowa 
Cedar  Rapids  

25,656 

32,811 

37,308 

Clinton  

22,698 

25,577 

27,386 

Council  Bluffs  

25,802 

29,292 

31,484 

Davenport  

35,254 

43,028 

48,811 

Des  Moines 

62,139 

86,368 

101,598 

Dubuque 

36,297 

38,494 

39,873 

Sioux  City    

33,111 

47,8"28 

57,078 

Waterloo  

12,580 

26,693 

35,559 

Kansas 
Kansas  City 

51,418 

82,331 

99,437 

Topeka 

33,608 

43,684 

48,726 

Wichita 

24,671 

52,450 

70,722 

Kentucky 
Covington  

42,938 

53,270 

57,144 

Lexington  

26,369 

35,099 

41,097 

Louisville 

204,731 

223,928 

238,910 

Newport  .  . 

28,301 

30,309 

31,927 

156 


POPULATION 


TABLE  27 

POPULATION  OF  UNITED  STATES  CITIES  HAVING,  IN 
1910,  25,000  INHABITANTS  OR  MORE  —  (Continued) 


1900. 

1910. 

1916  (estimate). 

(1) 

(2) 

(3) 

(4) 

Louisiana 
New  Orleans  
Shreveport  

287,104 
16,013 

339,075 
28,015 

371,747 
35,230 

Maine 
Lewiston  .  . 

23,761 

26,247 

27809 

Portland  .... 

50,145 

58,571 

63867 

Maryland 
Baltimore  

508,957 

558,485 

589,621 

Massachusetts 
Boston 

560892 

670585 

756  476 

Brockton  

40,063 

56,878 

67,449 

Brookline  (town) 

19,935 

27,792 

32730 

Cambridge.  .  .  . 

91,886 

104,839 

112981 

Chelsea  

34,072 

32,452 

46,192 

Chicopee  

19,167 

25,401 

29,319 

Everett 

24336 

33484 

39  233 

Fall  River  

104,863 

119,295 

128,366 

Fitchburg 

31,531 

37  826 

41  781 

Haverhill  . 

37,175 

44,H5  • 

48477 

Holyoke  , 

45,712 

57,730 

65286 

Lawrence  

62,559 

85,892 

100,560 

Lowell 

94969 

106  294 

113  245 

Lynn 

68513 

89336 

102  425 

Maiden 

33,664 

44,404 

51  155 

New  Bedford  .  .  . 

62,442 

96,652 

118  158 

Newton  
Pittsfield  
Quincy 

33,587 
21,766 
23899 

39,806 
32,121 
32642 

43,715 
38,629 
38  136 

Salem  . 

35956 

43  697 

48562 

Somerville  
Springfield  .  .  .  :  
Taunton  
Waltham 

61,643 
62,059 
31,036 
23  481 

77,236 
88,926 
34,259 
27  834 

87,039' 
105,942 
36,283 
30570 

Worcester   .  . 

118421 

145  986 

163  314 

Michigan 
Battle  Creek    

18,563 

25,267 

29  480 

Bay  City  
Detroit  

27,628 
285,704 

45,166 
465,766 

47,942 
571,784 

Flint 

13  103 

38550 

54  772 

Grand  Rapids 

87,565 

112,571 

128  291 

POPULATION  OF  UNITED  STATES  CITIES         157 


TABLE  27 

POPULATION  OF  UNITED  STATES  CITIES  HAVING,  IN 
1910,  25,000  INHABITANTS  OR  MORE  —  (Continued) 


1900. 

1910. 

1916  (estimate). 

(1) 

(2) 

(3) 

(4) 

Michigan  —  (Continued) 
Jackson  

25,180 

31,433 

35,363 

Kalamazoo 

24404 

39  437 

48886 

Lansing 

16485 

31  229 

41,698 

Saginaw 

42,345 

50510 

55,642 

Minnesota 
Duluth                       

52,969 

78,466 

94,495 

Minneapolis  

202,718 

301,408 

363,454 

St.  Paul  

163,065 

214,744 

247,232 

Missouri 
Joplin  

26,023 

32,073 

33,216 

Kansas  City 

163  752 

248  381 

297  847 

St.  Joseph 

102  979 

77  403 

85236 

St.  Louis  .  . 

575238 

687029 

757309 

Springfield 

23,267 

35201 

40341 

Montana 
Butte  

30,470 

39,165 

43,425 

Nebraska 
Lincoln  

40,169 

43,973 

46.515 

Omaha 

102  555  - 

124096 

165  470 

South  Omaha 

26001 

26259 

New  Hampshire 
Manchester  

56,987 

70063 

78283 

Nashua  

23,898 

26,005 

27,327 

New  Jersey 
Atlantic  City  

27,338 

46,150 

57,660 

Bayonne 

32722 

55  545 

69  893 

Cam  den  .    .    . 

75935 

94538 

106  233 

East  Orange  

21  506 

34371 

42458 

Elizabeth  

52,130 

73,409 

86690 

Hoboken 

59  364 

70  324 

77  214 

Jersey  City.  . 

206  433 

267  779 

306  345 

Newark  

246  070 

347  469 

408  894 

Orange  

24,141 

29  630 

33  080 

Passaic  

27,777 

54,773 

71  744 

Paterson 

105  171 

125  600 

138  443 

Perth  Amboy 

17  699 

32  121 

41  185 

Trenton.  . 

73,307 

96  815 

111  593 

West  Hoboken  (town)  .... 

23,094 

35,403 

43,139 

158 


POPULATION 


TABLE  27 

POPULATION  OF  UNITED  STATES  CITIES  HAVING,  IN 
1910,  25,000  INHABITANTS  OR  MORE  —  (Continued) 


1900. 

1910. 

1916  (estimate). 

(1) 

(2) 

(3) 

(4) 

New  York 
Albany          

94,151 

100,253 

106,003 

Amsterdam  

20,929 

31,267 

37,103 

Auburn  
Binghamton  

30,345 
39,647 

34,668 
48,443 

37,385 
53,973 

Buffalo  

352,387 

423,715 

468,558 

Elmira 

35,672 

37,176 

38,120 

Jamestown 

22,892 

31,297 

36,580 

Kingston 

24,535 

25,908 

26,771 

Mount  Vernon     

21,288 

30,919 

37,009 

New  Rochelle  '.  
New  York  
Manhattan  Borough  
Bronx  Borough  
Brooklyn  Borough 

14,720 
3,437,202 
1,850,093 
200,507 
1,166,582 

28,867 
4,766,883 
2,331,542 
430,980 
1,634,351 

37,759 
5,602,841 
575,876 
1,928,734 
2,634,224 

Queen's  Borough 

152,999 

284,041 

366,126 

Richmond  Borough  
Newburgh  
Niagara  Falls  

67,021 
24,943 
'      19,457 

85,969 
27,805 
30,445 

97,881 
29,603 
37,353 

Poughkeepsie  
Rochester 

24,029 
162,608 

27,936 
218,149 

30,390 
256417 

Schenectady  

31,682 

72,826 

99,519 

Syracuse  
Troy  

108,374 
60,651 

137,249 
76,813 

155,624 
77,916 

Utica 

56383 

74419 

87  401 

Watertown 

21,696 

26730 

29894 

Yonkers            .... 

47,931 

79,803 

99838 

North  Carolina 
Charlotte  

18,091 

34,014 

39,823 

Wilmington  •. 
Ohio 
Akron 

20,976 

42728 

25,748 
69067 

29,892 
85625 

Canton  
Cincinnati  
Cleveland  
Columbus 

30,667 
381,768 
381,768 
125  560 

50,217 
560,663 
560,663 
181  511 

60,852 
410,476 
674,073 
214  878 

Dayton 

85333 

116577 

127  224 

Hamilton.  .         

23,914 

35,279 

40496 

Lima  
Lorain  

21,723 
16,028 

30,508 
28,883 

35,384 
36,964 

POPULATION  OF  UNITED  STATES  CITIES         159 


TABLE  27  ' 

POPULATION  OF  UNITED  STATES  CITIES  HAVING,  IN 
1910,  25,000  INHABITANTS  OR  MORE  —  (Continued) 


1900. 

1910. 

1916  (estimate). 

(1) 

(2) 

(3) 

(4) 

Ohio  —  (Continued) 
Newark  .... 

18,157 

25,404 

29,635 

Springfield  

38,253 

46,921 

51,550 

Toledo  

131,822 

168,497 

191,554 

Youngstown  
Zanesville  

44,885 
23,538 

79,066 
28,026 

108,385 
30,863 

Oklahoma 
Muskogee 

4,254 

25,278 

44,218 

Oklahoma  City 

10,037 

64,205 

92,943 

Oregon 
Portland   .  .  . 

90,426 

207,214 

295,463 

Pennsylvania 
Allentown  

35,416 

51,913 

63,505 

Altoona  

38,973 

52,127 

58,659 

Chester 

33988 

38537 

41  396 

Easton  

25,238 

28,523 

30,530 

Erie 

52733 

66,525 

75,195 

Harrisburg 

50,167 

64,186 

72,015 

Hazleton 

14,230 

25,452 

28,491 

Johnstown 

35,936 

55,482 

68,529 

Lancaster  . 

41,459 

47,227 

50,853 

McKeesport  .  .  . 

34,227 

42,694 

47,521   . 

Newcastle  

28,339 

36,280 

41,133 

Norristown  (borough)  
Philadelphia  :  .  . 

22,265 
1,293,697 

27,875 
1,549,008 

31,401 
1,709,518 

Pittsburgh  
Reading 

451,512 
78,961 

533,905 
96,071 

579,090 
109,381 

Scranton 

102,026 

129,867 

146,811 

Shenandoah  (borough)  .  .  . 
Wilkes-Barre  
Williamsport  
York 

20,321 
51,721 

28,757 
33,708 

25,774 
67,105 
31,860 
44,750 

29,201 
76,776 
33,809 
51,656 

Rhode  Island 
Newport        .       .    . 

22,441 

27,149 

30,108 

Pawtucket  
Providence  

39,231 
175,597 

51,622 
224,326 

59,411 
254,960 

Warwick  (town)  
Woonsocket 

21,316 
28,204 

26,629 
38,125 

29,969 
44,360 

South  Carolina 
Charleston 

55,807 

58,833 

60,734 

160 


POPULATION 


'  TABI^E  27 

POPULATION  OF  UNITED   STATES  CITIES  HAVING,  IN 
1910,   25,000  INHABITANTS  OR  MORE—  (Concluded) 


1900. 

1910. 

1916  (estimate). 

(1) 

(2)        . 

(3) 

(4) 

SouthCarolina  —  (Continued) 
Columbia 

21,108 

26319 

34,611 

Tennessee 
Chattanooga 

30,154 

44,604 

60,075 

Knoxville 

32,637 

36,346 

38,676 

Memphis  

102,320 

131,105 

148,995 

Nashville  

80,865 

110,364 

117,057 

Texas 
Austin 

22258 

29  860 

34814 

Dallas 

42638 

92  104 

124  527 

El  Paso 

15906 

39  279 

63  705 

Fort  Worth 

26688 

73  312 

104  562 

Galveston.  . 

37,789 

36981 

41  863 

Houston  

44633 

78,800 

112,307 

San  Antonio  

53,321 

96,614 

123,831 

Waco.., 

20,686 

26,425 

33,385 

Utah 
Ogden 

16313 

25580 

31  404 

Salt  Lake  City 

53531 

92777 

117  399 

Virginia 
Lynchburg  

18,891 

29  494 

32940 

Norfolk  

46,624 

67  452 

89  612 

Portsmouth  

17,427 

33,190 

39  651 

Richmond  

85,050 

127,628 

156,687 

Roanoke 

21  495 

34  874 

43  284 

Washington 
Seattle  

80671 

237  194 

348  639 

Spokane  

36848 

104402 

150  323 

Tacoma 

37  714 

83  743 

112  770 

West  Virginia 
Huntington 

11  923 

31  161 

45  629 

Wheeling  . 

38  878 

41  641 

43  377 

Wisconsin 
Green  Bay  

18,684 

25  236 

29353 

La  Crosse 

28  895 

30  417 

31  677 

Madison 

19  164 

25  531 

30  699 

Milwaukee 

285  315 

373  857 

436  535 

Oshkosh  

28'  284 

33  062 

36  065 

Racine  

29,102 

38002 

46486 

Sheboygan  

22,962 

26398 

28  559 

Superior 

31  091 

40  384 

46  266 

COLOR  OR  RACE,   NATIVITY  AND  PARENTAGE      161 

Metropolitan  districts.  —  For  some  purposes  the  popula- 
tion of  a  city  plus  its  adjacent  suburbs  is  of  more  importance 
than  that  of  the  city  itself.  During  recent  years  the  growth 
of  the  suburbs  has  often  been  much  greater  than  that  of  the 
city  itself.  This  subject  is  discussed  in  U.  S.  Census,  1910, 
Population,  Vol.  I,  p.  74. 

In  1910,  New  York  City  had  a  population  of  4,766,883, 
the  adjacent  territory,  1,863,716,  or  39  per  cent  of  the  city's 
population.  During  the  last  decade  the  city  increased  38.7 
per  cent  and  the  adjacent  territory  45.5  per  cent. 

In  Boston  the  city's  population  was  560,892,  that  of  the 
adjacent  territory,  708,492,  or  126  per  cent  of  the  city's 
population. 

Classification  of  population.  —  One  of  the  greatest  mis- 
takes which  health  officers  make  is  failure  to  take  into 
account  the  make-up  of  the  population.  Two  places  cannot 
be  fairly  compared  as  to  death-rate  or  birth-rate,  unless 
the  composition  of  the  population  in  the  places  is  substan- 
tially the  same.  This  point  will  be  emphasized  again  in 
Chapter  VII. 

In  many  demographic  studies  it  is  necessary  to  take  into 
account  age,  sex,  and  nationality  as  primary  factors;  and  at 
times  also  such  matters  as  marital  condition,  school  attend- 
ance, illiteracy,  ownership  of  homes,  occupation,  and 
so  on. 

It  will  not  be  possible  in  this  volume  to  go  into  all  of  these 
classifications.  They  should  be  carefully  studied,  however, 
from  the  census  reports  themselves.  Every  health  officer 
should  know  the  composition  of  the  people  in  the  city  or 
district  under  his  jurisdiction. 

Color  or  race,  nativity  and  parentage.  —  The  racial 
composition  of  the  United  States  has  changed  materially  in 
fifty  years.  This  is  well  illustrated  by  Fig.  36.  In  1850 
about  three-quarters  of  the  people  were  native  whites,  now 


162 


POPULATION 


1850 


1860 


1870 


FIG.  36.  —  Racial  Composition  of  Population  of  the  United  States. 


SEX  DISTRIBUTION 


163 


only  about  one-half.     There  are  great  differences  in  different 
cities  and  states. 

According  to  the  U.  S.  Bureau  of  the  Census  the  popula- 
tion is  divided  into  six  classes:  (1)  white,  (2)  negro,  (3) 
Indian,  (4)  Chinese,  (5)  Japanese  and  (6)  "all  others."  The 
white  population  is  subdivided  into : 

a.   Native,  native  parentage,  having  both  parents  born 

in  the  United  States. 

6.   Native,  foreign  parentage,  having  both  parents  born 
in  foreign  countries. ' 

c.  Native,  mixed  parentage,  having  one  native  parent 

and  the  other  foreign  born. 

d.  Foreign  born. 

It  is  often  desirable  to  subdivide  the  foreign  born  accord- 
ing to  the  countiy  from  which  they  came.  This  is  true  also 
of  the  parents. 

Sex  distribution.  —  There  are  two  ways  in  which  the 
sexes  are  compared,  —  one  is  to  compute  the  percentage 
which  the  number  of  each  sex  is  of  the  total  population,  the 
other  is  to  compute  the  ratio  of  males  to  females.  Thus,  we 
have  the  following  figures  for  1910: 


TABLE  28 
COMPARISON  OF  SEXES  IN  THE  UNITED  STATES 


Per 

cent. 

Males  to 

United  States. 

Male. 

Female. 

100  females. 

(D 

(2) 

(3) 

(4) 

Total  population                            

51.5 

48.5 

106.2 

Native  white,  native  parentage  
Native  white,  mixed  parentage  
Native  white  foreign  parentage   .  . 

51.0 
49.6 
50.0 

49.0 
50.4 
50.0  ' 

104.1 
98.4 
100.0 

Foreign  born  white                          

56.4 

43.6 

129.3 

164  POPULATION 

In  most  parts  of  the  country  males  are  in  excess,  and  gen- 
erally speaking  the  ratio  of  males  to  females  increases  from 
east  to  west.  In  only  a  few  states  do  we  find  females  in 
excess.  One  of  these  is  Massachusetts,  where  in  1910  the 
ratio  was  only  96.6.  In  Nevada,  on  the  other  hand,  the 
ratio  was  181.5,  not  very  far  from  two  men  to  one 
woman. 

Sex  distribution  ought  to  be  studied  in  connection  with  age 
distribution. 

Dwellings  and  families.  —  A  knowledge  of  the  number  of 
persons  in  a  dwelling  or  a  family  is  of  sociological  interest, 
and  it  may  be  of  practical  use  in  estimating  the  population 
of  an  area  the  boundaries  of  which  are  not  coincident  with 
any  civil  division.  Here  we  come  again  to  the  difficulty  of 
definition.  What  is  a  dwelling?  What  is  a  family?  A 
dwelling-house  is  considered  to  be  "a  place  where  one  or 
more  persons  regularly  sleep."  A  family  is  "a  household  or 
group  of  persons  who  live  together,  usually  sharing  the  same 
table."  This  includes  both  private  families,  consisting  of 
persons  related  by  blood,  and  economic  families. 

The  ideal  family  has  been  said  to  consist  of  a  father  and 
mother  and  three  children  with  an  occasional  grandfather  or 
grandmother,  aunt  or  uncle.  In  the  United  States  in  1910 
the  average  number  of  persons  to  a  family  was  only  4.5,  — 
apparently  much  smaller  than  the  ideal  The  average 
number  of  persons  to  a  dwelling  was  5.2.  Figures  for  differ- 
ent parts  of  the  country  are  given  in  Table  29. 

For  housing  problems  it  is  not  enough  to  know  that  the 
average  number  of  persons  per  dwelling  is  5.2.  This  extra 
two-tenths  of  a  person  is  difficult  to  place.  We  need  to 
know  how  many  dwellings  contain  one  person,  how  many 
two  persons,  and  how  many  three,  four,  five,  six,  and  so 
on.  It  is  difficult  to  secure  these  data. 


AGE  DISTRIBUTION 


165 


TABLE  29 
SIZE  OF  FAMILIES  AND  HOUSEHOLDS 


Place. 

Persons  per 
dwelling. 

Persons  per 
family. 

Families  per 
dwelling. 

(1) 

(2) 

(3) 

(4) 

United  States  

5.2 

4  5 

1  15 

Urban  

5.9 

4.5 

.31 

Rural  

4.7 

4.6 

.02 

New  England  

6.0 

4.5 

.33 

Urban  

6.5 

4.6 

.41 

Rural  
New  York  City  
Borough  of  Manhattan.  .  .  . 
Boston 

4.2 
15.6 
30.9 
9  1 

4.0 

4.7 
4.7 
4  8 

.05 
.32 

.58 
90 

Cambridge  Mass.    .           ( 

7  2 

4  6 

57 

Los  Angeles,  Cal.  . 

4.6 

4.1 

.12 

Spokane,  Wash. 

5.1 

4.6 

.11 

Age  distribution.  —  We  now  come  to  what  is  a  most 
important  division  of  the  population,  namely  separation  into 
age-groups.  In  connection  with  a  study  of  death-rates  and 
causes  of  death  a  knowledge  of  age  distribution  is  funda- 
mental. As  a  factor  in  vital  statistics  it  is  more  important 
than  sex  or  nationality  or  parentage  or  occupation  or  any 
other  particular  characteristic. 

In  taking  a  census  it  is  impossible  to  find  the  exact  age  of 
every  person  in  a  community,  and  even  if  this  could  be  done 
it  would  be  impracticable  to  arrange  the  people  in  groups, 
varying  by  short  intervals  of  tune.  Infants  and  young 
children  may  be  grouped  by  their  age  in  weeks  or  months, 
but  older  persons  are  seldom  divided  into  groups  for  which 
the  time  interval  is  less  than  one  year.  Five-year  and  ten- 
year  groups  are  even  more  commonly  used.  In  this  chapter 
we  shall  not  consider  smaller  subdivisions  than  one  year. 
The  ages  of  infants  will  be  taken  up  in  the  chapter  which 
treats  of  infant  mortality. 


166  POPULATION 

Census  meaning  of  age.  —  If  we  wish  to  state  a  person's 
age  in  years,  using  a  whole  number,  we  may  do  so  in  one  of 
two  ways;  we  may  give  the  age  as  that  of  the  last  birthday  or 
as  that  of  the  nearest  birthday.  The  difference  is  by  no 
means  insignificant  in  the  case  of  children,  for  the  difference 
of  half  a  year  would  represent  a  large  percentage  of  the  age. 
In  some  parts  of  the  world  the  next  birthday  is  often  stated 
as  the  age,  an  infant  being  regarded  as.  one  year  of  age  even 
though  he  had  been  born  only  an  hour.  In  the  Orient  age 
has  to  do  also  with  the  calendar  year  in  which  the  child 
was  born.  A  child  born  in  November  might  in  December 
be  called  a  year  old,  but  after  January  first  might  be  called 
two  years.  These  curious  customs  ought  to  be  known  by 


Grouping  by  last  Birthdays 
0  +  1+  2  +  3  + 


r~ 

Y 

Y 

^ 

Y~ 

\ 

V                                 J 

V                                            J 

L                                       ^ 

^                                 j 

v_ 

J 

Y 

2 

IT 

3 

Y 

4 

Y 

5 

0             1 

Grouping  by  nearest  Birthdays 
FIG.  37.  —  Age-Grouping  by  Years. 

those  enumerating  the  ages  of  persons  in  the  foreign  quarters 
of  our  cities  and  justify  the  check  question  asked  by  census 
enumerators,  namely,  the  date  of  birth. 

The  last  birthday  method  was  used  in  the  United  States 
census  of  1910, 1900  and  1880;  it  is  the  method  used  in  Eng- 
land. In  1890,  however,  the  nearest  birthday  was  used.  The 
effect  of  the  definition  of  age  on  the  age-grouping  will  be  ap- 
parent from  the  following  diagram:  The  nearest  birthday 
method  creates  confusion  in  the  ages  of  infants  and  children 
one  year  old.  If  infants  include  children  up  to  the  age  of  one 
year,  then  the  "one-year"  group  must  be  limited  to  half  a 
year  or  else  there  is  duplication  of  those  between  six  months 


ERRORS  IN  AGES  OF  CHILDREN 


167 


and  one  year.  The  discrepancies  in  the  1890  figures  are 
plainly  shown  by  the  following  table  which  gives  the  per- 
centage distribution  of  the  population  under  five  years  of 
age. 

TABLE  30 

PER  CENT  DISTRIBUTION  OF  POPULATION  UNDER 
5  YEARS  OF  AGE 


Age  in  years. 

"  Nearest 
birthday." 

"  Last  birthday." 

1890. 

1880. 

1900. 

1910. 

(1) 

(2) 

(3) 

(4) 

(5) 

Under  1  year 
1  + 
2+ 
3  + 
4+ 
Total  under  5  years 

Per  cent. 
20.5 
14.1 
22.7 
21.4 
.     21.3 

Per  cent. 
.  20.9 
18  2 
20  6 
20.0 
20.3 

Per  cent. 
20.9 
19.3 
20.0 
19.9 
20.0 

Per  cent. 
20.9 
18  6 
20.4 
20.3 
19.9 

100.0 

100.0 

100.0 

100.0 

The  small  number  in  the  one-year  group  and  the  large 
number  in  the  two-year  group  in  1890  should  be  noticed. 

Errors  in  ages  of  children.  —  The  above  table  shows  that 
even  by  the  last-birthday  method  the  age  distribution  of 
children  in  one-year  groups  was  unsatisfactory.  Normally 
there  are  more  children  under  one  year  of  age  than  between 
one  and  two  years,  more  between  one  and  two  than  between 
two  and  three  and  more  between  thcee  and  four  than  between 
four  and  five.  Yet  in  1910  the  one-year  group  contained 
fewer  than  the  two-year  group,  and  in  1900  the  3+  year 
group  contained  fewer  than  the  4+  year  group. 

These  discrepancies  are  due  to  errors.  They  are  greatest 
in  populations  wheVe  there  is  much  illiteracy  and  where  no 
attempt  is  made  to  check  the  age  returns  by  asking  the  date 
of  birth.  Thus  we  may  compare  the  data  for  Germany 
(1900)  and  the  negro  population  of  the  United  States  (1910). 


168 


POPULATION 


TABLE  31 

PERCENTAGE  DISTRIBUTION   OF  POPULATION 
UNDER  6  YEARS 


Age. 

Germany. 

United  States 
(Negro  population.) 

(1) 

(2) 

(3) 

0+ 

20.6 

20.0 

1+ 

20.3 

17.4 

2+ 

20.2 

20.6 

3+ 

19.5 

20.9 

4+ 

19.3 

21.1 

Under  5 

100.0 

100.0 

Errors  due  to  use  of  round  numbers.  —  An  important 
source  of  error  in  age  statistics  is  that  of  mixing  round 
numbers  with  more  accurate  figures.  In  replying  to  the 
enumerator's  questions  concerning  age  most  persons  will 
state  their  age  accurately,  but  some  will  give  the  nearest 
round  number.  An  ignorant  or  careless  person  who  may  be 
39  or  41  years  old  may  give  his  age  as  40,  a  figure  which  in 
his  mind  is  near  enough.  This  habit  is  encouraged  by  ask- 
ing for  the  "nearest  birthday"  as  was  done  in  1890.  In  most 
censuses  there  are  enough  instances  of  this  sort  to  produce 
noticeable  concentrations  around  the  ages  ending  in  0  or  5. 
This  is  well  illustrated  by  Fig.  38,  which  shows  the  popula- 
tion of  Massachusetts  males  in  1905  distributed  by  groups. 
This  error  of  round  numbers  is  by  no  means  confined  to  the 
subject  of  age.  It  is  met  with  in  all  sorts  of  statistical  work. 
Dates  are  often  stated  as  "the  first  of  the  month,"  or  the 
tenth  or  the  fifteenth.  These,  mixed  with  more  accurate 
statements,  may  produce  abnormal  concentrations.  Methods 
of  adjusting  data  troubled  with  these  concentrations  on  the 
round  numbers  are  used  by  statisticians  and  are  referred  to 
in  Chapter  XIV. 


ERRORS  DUE  TO  USE  OF  ROUND  NUMBERS     169 


The  U.  S.  Census  Bureau  in  studying  the  error  due  to  the 
abnormal  use  of  round  numbers  has  made  use  of  a  measure 
termed  the  "  Index  of  Concentration."  This  was  taken  to 
be  the  "per  cent  which  the  number  reported  as  multiples  of 


k 


AGE  DISTRIBUTION 

IN 

MASSACHUSETTS 
FROM   1905  STATE  CENSUS 

VOLUME  1,  POPULATION 
AND  SOCIAL  STATISTICS,  P.  555 


i 


10  20  30  40  50  60 

Age  in  Years 

FIG.  38.  —  Age  Distribution  in  Massachusetts. 


70 


5  forms  of  one-fifth  of  the  total  number  between  ages  23  to 
62  years,  inclusive."  Thus  in  the  U.  S.  there  were  43  million 
persons  aged  23  to  62  years.  One-fifth  of  these  would  be  8.6 
million.  The  total  number  of  persons  aged  23  to  62  whose 
age  was  reported  as  a  multiple  of  5  was  10.3  million.  Hence 
the  index  of  concentration  was  10.3  -f-  8.6,  or  120. 


170 


POPULATION 


It  was  found  that  the  index  of  concentration  increased 
directly  with  the  ignorance  and  illiteracy.  For  the  native 
white  persons  it  was  112;  for  foreign  born  whites,  129; 
for  colored  persons,  153.  It  is  interesting  to  compare  these 
figures  for  those  of  certain  other  countries. 

TABLE  32 
ERRORS  OF  REPORTING  AGE 


Country. 

Date. 

Index  of  concen- 
tration. 

(1) 

(2) 

(3) 

Belgium  

1900 

100 

England  and  Wales 

1901 

100 

Sweden 

1900 

101 

German  Empire    .   . 

1900 

102 

France  

1901 

106 

Canada  

1881 

110 

Hungary  

1900 

133 

Russian  Empire  

1897 

182 

Bulgaria  

1905 

245 

Other  sources  of  error.  —  Besides  ignorance  as  to  age 
there  are  other  sources  of  error.  One  of  these  is  deliberate 
under-estimate  of  age,  most  conspicuous  among  middle-aged 
women.  Another  is  over-estimate,  most  conspicuous  among 
the  aged.  The  latter  is  of  relatively  little  weight,  but  the 
former  tends  to  overload  the  early  ages  of  adult  life. 

Age  groups.  —  The  primary  tabulations  of  the  census 
give  the  ages  of  the  people  by  single  years.  For  practical 
use  and  for  application  to  particular  localities  it  is  necessary 
to  combine  them  into  groups  of  five,  ten,  or  twenty  years,  or 
other  groups  suitable  to  particular  needs.  There  appears 
to  be  no  recognized  standard  of  age  grouping,  and  perhaps 
this  is  not  desirable  as  there  are  many  different  uses  to  which 
the  figures  are  put. 


PERSONS  OF  UNKtfOWlSr  AGE  171 

The  U.  S.  Census  states  the  boundaries  of  the  groups  in 
inclusive  numbers,  such  as  CM:;  5-9;  10-14;  etc.,  and  not 
in  round  numbers,  as  0-5;  5-10;  10-15.  With  the  original 
age  records  given  in  years  it  is  undoubtedly  the  most  exact 
method. 

A  grouping  largely  used  in  the  1910  census  was  the  fol- 
lowing : 

Under  5  Years 

(Under  1  Year) 

5-9 

10-14 

15-19 

20-24 

25-34 

35-44 

45-64 

65  and  over 
Age  unknown 

In  this  arrangement  we  have  one-year  groups  from  ages 
one  to  five,  5-year  groups  from  ages  five  to  twenty-five, 
10-year  groups  from  twenty-five  to  forty-five,  and  above 
that  twenty-year  groups. 

Persons  of  unknown  age.  —  One  of  the  puzzling  things 
about  age  distribution  is  to  know  how  to  treat  the  "age 
unknown."  Usually  this  number  is  not  large,  but  in  par- 
ticular cases  it  may  be.  In  1910  only  0.18  per  cent  of  the 
people  of  the  United  States  were  included  in  this  group,  and 
in  1900  only  0.26  per  cent. 

One  way  is  to  place  them  in  a  group  by  themselves,  letting 
the  size  of  the  group  stand  as  a  sort  of  test  of  the  accuracy 
of  the  investigation.  On  the  whole  this  is  probably  the  best 
thing  to  do. 

Another  way  would  be  to  distribute  the  unknowns  pro 
rata  through  the  other  groups.  But  there  is  really  no  justi- 


172 


POPULATION 


fi cation  for  doing  so,  because  the  persons  of  unknown  age 
may  be  confined  to  certain  selected  ages,  as  the  very  old. 

Redistribution  of  population.  —  If  the  ages  of  the  people 
are  tabulated  by  years  it  is  of  course  easy  to  combine  them 
into  any  desired  age  groups;  but  if  the  data  are  tabulated 
according  to  one  age-grouping  and  it  is  desired  to  ascertain 
the  numbers  in  other  age-groups  the  problem  is  more  difficult. 
Approximate  results  only  can  be  expected  and  these  can  be 
obtained  by  graphical  methods  or  by  computation. 

For  this  purpose  the  summation  diagram  is  most  convenient. 

In  1910  the  population  of  Cambridge  was  as  follows: 


TABLE  33 
POPULATION  OF  CAMBRIDGE,  MASS.,  BY  AGE-GROUPS 


Persons  less  than  stated  age. 

Age-group. 

Number. 

Age. 

Number. 

Per  cent. 

(1) 

(2) 

(3) 

(4) 

(5)     ' 

0-1 

2,323 

1 

2,323 

2.3 

1-4 

8,479 

5 

10,802 

10.4 

5-9 

9,471 

10 

20,273 

19.4 

10-14 

8,892 

15 

29,165 

27.9 

15-19 

8,930 

20 

37,095 

36.4 

20-24 

10,408 

25 

47,503 

46.4 

2^-34 

19,175 

35 

66,678 

64.6 

35-44 

15,726 

45 

82,404 

79.6 

45-64 

16,732 

65 

99,136 

95.6 

65-99 

4,642 

100 

104,778 

99.4 

Unknown 

61 



61 

0.6 

Total 

104,839 

104,839 

100.0 

The  figures  in"  column  (4)  are  plotted  in  Fig.  39.  Let  us 
suppose  that  we  desire  to  obtain  the  number  of  persons  in 
age-group  23-27  inclusive.  The  diagram  shows  that  about 
43,500  were  less  than  23  years  old  and  about  53,500  less  than 


REDISTRIBUTION  OF  POPULATION 


173 


-Sr< 

d 


10 


20 


30 


40  50          60 

Age  in  Years 


70 


80 


90 


100 


FIG.  39.  —  Age  Distribution  of  Population  shown  by  Summation 
Curve,  Cambridge,  Mass.:  1910. 

28  years  old.    The  group,  therefore,  contains  53,500  -  43,500, 
or  10,000. 

In  making  a  complete  redistribution  of  the  population  in 
new  age-groups  it  is  well  to  check  the  results  by  adding  them 
together  to  see  that  they  equal  the  total.  The  accuracy  of 
the  result  will  depend  upon  the  scale  used  for  plotting  and 
the  smoothness  of  the  curve. 


174  POPULATION 

We  might  compute  the  number  of  persons  in  age-group 
23-27  as  follows: 

10,408  X    f  =  4163 

19,175  X  i\f  =  5753 

99l6 

This  assumes  a  uniform  age  distribution  within  each  age- 
group,  which  is  not  strictly  correct. 

Redistribution  of  population  for  non-censal  years.  —  In 
the  case  of  non-censal  years  the  method  of  redistribution  of 
population  is  essentially  the  same  as  that  just  described  but 
there  are  three  steps  to  the  process. 

The  first  step  is  to  estimate  the  total  population  for  the 
year  in  question  by  methods  already  described. 

The  second  step  is  to  find  the  percentage  distribution  of 
the  population  as  it  was  at  the  time  of  the  nearest  census. 
As  a  rule  the  percentage  composition  of  a  population  by  age- 
groups  does  not  change  rapidly  from  year  to  year.  For  an 
intercensal  year  it  would  be  possible  to  find  the  percentage 
distribution  for  both  the  preceding  and  following  census 
and  by  interpolation  obtain  more  accurate  percentages  for 
the  intercensal  years.  The  use  of  the  summation  curve  is 
the  most  convenient  method  however. 

The  third  step  is  to  multiply  the  estimated  total  popu- 
lation by  the  percentage  obtained  in  the  second  step. 
The  feature  of  this  problem  obviously  lies  in  the  second 
step. 

Let  us  try  to  find  the  age  distribution  of  the  population 
of  Cambridge  in  the  year  1906.  In  addition  to  the  above 
figures  for  1910  we  have  also  from  the  census  records  the 
following  figures  for  1900: 


PROGRESSIVE  CHARACTER  OF  AGE  DISTRIBUTION     175 


TABLE  34 

ESTIMATES  OF  POPULATION  BY  AGE-GROUPS  FOR  A 
NON-CENSAL  YEAR:   CAMBRIDGE,  MASS. 


Persons  less  than  stated  age. 

Number 

Aee 

Number. 

Per  cent. 

(1) 

(2) 

(3) 

(4) 

(5) 

0-1 

2,123 

1 

2,123 

2.3 

1-4 

7,519 

5 

9,642 

10.5 

5-9 

8,343 

10 

17,985 

19.6 

10-14 

7,331 

15 

25,316 

27.5 

15-19 

7,781 

20 

33,097 

36.0 

20-24 

10,588 

25 

43,685 

47.5 

25-29 

9,973 

30 

53,658 

58.4 

30-34 

8,157 

35 

61,815 

67.3 

35-44 

12,377 

45 

74,192 

78.5 

45-54 

8,561 

55 

82,753 

90.0 

55-64 

5,028 

65 

87,781 

95.5 

65-99 

3,652 

100 

91,433 

99.4 

Unknown 

453 

453 

Total 

91,886 

91,886 



The  percentage  distribution  for  1900  and  1910  are  both 
shown  on  Fig.  40.  It  will  be  noticed  that  the  two  curves 
coincide  for  the  upper  and  lower  ages,  but  not  for  the  middle 
ages.  For  the  year  1906  the  percentages  to  be  used  would 
naturally  lie  somewhere  between  the  two. 

Progressive  character  of  age  distribution.  —  Among  the 
causes  of  the  variation  of  death-rates  from  year  to  year  is  the 
progressive  change  in  age  distribution.  We  often  overlook 
this.  We  know  that  individuals  grow  old,  but  we  forget  that 
the  10  year  old  children  of  today  will  be  20  years  old  ten 
years  hence,  and  30  years  old  ten  years  later  and  so  on.  We 
are  less  wise  than  the  motley  fool  who  said: 

"It  is  ten  o'clock: 

'Tis  but  an  hour  ago  since  it  was  nine, 
And  after  one  hour  more  'twill  be  eleven; 
And  so  from  hour  to  hour,  we  ripe  and  ripe, 
And  then,  from  hour  to  hour,  we  rot  and  rot; 
And  thereby  hangs  a  tale." 


176  POPULATION 

While  the  age  distribution  of  a  population  does  not  changi 
rapidly  from  year  to  year  yet  it  does  change.  This  is  strik 
ingly  shown  by  the  statistics  of  Sweden  from  1750  to  1900 


100 
90 
80 
70 

60 

-P 

250 

fi 

40 
30 
20 
10 

0 

( 

TT—~ 

~.  —  • 

..  - 

—  ^( 

/ 

**^ 

f 

/ 

/ 

A 

' 

a  t 

t 

W) 

/ 

M 

// 

< 
j 

r 

7 

/ 

7 

/ 

f 

/ 

' 

J 

/ 

/ 

)     10     20     30    40     50    60     70    80     90    10 

Age  ia  Years 

FIG.  40.  — Percentage  Age  Distribution  of  Population,  Cambridge, 
Mass.,  showing  slight  differences  in  ten  years. 

During  this  interval  there  was  but  little  emigration  or  immi 
gration,  but  the  birth-rate  varied  considerably.  In  Fig 
41,  the  population  data  are  plotted  for  five-year  groups  am 
for  five-year  intervals  of  time;  consequently  the  persons  wh< 


PROGRESSIVE  CHARACTER  OF  AGE  DISTRIBUTION     177 

appeared  in  the  0-4-group  at  one  date  would  appear  in  the 
5-9-group  five  years  later,  except  as  losses  by  death  occurred. 
It  is  interesting  to  see  how  the  influences  which  increase  or 
decrease  the  numbers  of  children  produce  results  which  flow 


FIG.  41.  —  Age  Distribution  of  the  People  of  Sweden  by  Five- 
Year  Groups:  1750-1900. 

as  waves  throughout  a  long  life-term.  For  example,  the 
high  birth-rate  between  1820  and  1825,  which  caused  a  peak 
in  the  0-4-group  in  1825,  caused  a  peak  in  the  5-9-group  in 
1830  and  this  could  be  traced  for  three-score  years  and  ten. 
In  the  same  way  the  trough  in  the  0-4  curve  in  1810  can  be 
followed  for  sixty  years. 


178 


POPULATION 


This  same  progressive  change  in  age  distribution  can  be 
observed  in  Massachusetts  in  spite  of  the  fact  that  the 
curves  are  confused  by  accessions  due  to  immigration.  The 
peak  in  the  0-4-group  in  1860  can  be  followed  for  fifteen 
years,  but  after  that  immigration  appears  to  control.  The 
immigration  peak  seen  in  the  2Q-24-group  in  1880  can  like- 
wise be  traced  almost  to  1910. 

This  progressive  change  of  age  is  very  important,  for  with 
constant  specific  death-rates  for  each  age  it  would  auto- 
matically control  the  general  death-rate.  It  shows  too  that 
a  loss  of  millions  of  young  men  in  the  present  Great  War  will 
profoundly  affect  the  age  distribution  of  the  nations  of  Europe 
for  half  a  century  to  come.  There  is  much  food  for  reflection 
in  this  study. 

Types  of  age  distribution.  —  According  to  Sundbarg  one 
of  the  striking  features  of  normal  age  distribution  is  the  fact 
that  about  one-half  of  the  population  are  between  15  and  50 
years  of  age.  He  distinguishes  three  types  of  age  distribu- 
tion. The  first  is  the  Progressive  Type,  the  second  the 
Stationary  Type,  and  the  third,  the  Regressive  Type.  These 
are  illustrated  by  the  following  typical  groupings: 


TABLE  35 
TYPES  OF  POPULATION 


Per  cent  of  population. 

years. 

Progressive 

Stationary 

Regressive 

type. 

type. 

type. 

(1) 

(2) 

(3) 

(4) 

0-14 

40 

33 

20 

15-49 

50 

50 

50 

50- 

10 

17 

30 

TYPES  OF  AGE  DISTRIBUTION 


179 


It  will  be  noticed  that  in  all  cases,  the  proportion  of  middle- 
aged  persons  is  the  same,  and  that  the  classification  depends 
upon  the  proportion  of  persons  under  15  years  of  age  to 
those  more  than  50  years  of  age. 

To  these  classes  might  be  added  two  more,  one  in  which 
a  population  has  lost  many  of  its  middle-aged  persons  by 
emigration  and  one  in  which  a  population  has  gained  by 
accessions  of  middle-aged  persons.  If  the  percentage  of 
persons  between  15  and  50  years  of  age  is  much  less  than  50 
it  indicates  that  the  place  has  lost  by  emigration  and  this  may 
be  termed  the  secessive  type;  while  if  the  percentage  of  per- 
sons between  15  and  50  years  of  age  is  greater  than  50  it  may 
be  termed  the  accessive  type. 

The  following  are  examples  of  age  distribution  on  the  basis 
of  this  classification: 


TABLE  36 
TYPES  OF  POPULATION  BASED   ON  AGE-GROUPING 


Per  cent  of  population. 

0-14 
years. 

15-49 
years. 

50  years 
and  over. 

(1) 

(2) 

(3) 

(4) 

Sweden  (1751-1900).    .  . 

33 
32 

27 
32 

27 
26 
27 
28 

46 
6 

50 
54 
57 
54 
58 
61 
51 
50 

48 
74 

17 
15 
16 
14 
15 
13 
22 
22 

-     6 
20 

United  States  (1910).  .  . 

Massachusetts  

Minnesota  

New  York  State  

Washington  State  

Maine 

Mass.,  native  white  of  native  parentage. 

Mass.,  native  white  of  foreign  or  mixed  par- 
entage   

Mass.,  foreign-born  white. 

180 


POPULATION 


It  will  be  seen  that  Sweden  has  a  normal  stationaiy  popu- 
lation, Massachusetts  has  an  accessive  population  with  57 
per  cent  between  15  and  50  years.  Washington  is  even  more 
accessive.  Maine  tends  to  be  regressive,  as  it  has  an  abnor- 
mally large  number  of  persons  over  50  years  of  age.  This  is 
also  the  case  with  the  population  of  native-white  parentage 
of  Massachusetts.  The  native-white  population  of  foreign 
or  mixed  parentage,  however,  is  decidedly  progressive. 

Standards  of  age  distribution.  —  For  purposes  of  com- 
putation and  comparison  it  is  often  convenient  to  have  some 
standard  of  age  distribution  which  can  be  used  as  a  basis  of 
reference.  Several  have  been  suggested. 

A  simple  one  was  the  actual  population  of  Sweden  in  1890. 
This  was  suggested  because  the  country  was  not  much  in- 
fluenced by  emigration  or  immigration.  This  standard  had 
only  five  groups.  It  was  this: 


TABLE  37 
AGE  DISTRIBUTION  OF  SWEDEN,   1890 


Age-group. 

Per  cent. 

(1) 

(2) 

0-1 
1-19 
20-39 
40-59 
60- 

2.55 
39.80 
26.98 
19.23 
11.46 

100.00 

STANDARD  MILLION 


181 


The  "Standard  Million,"  namely  the  population  of  Eng- 
land and  Wales  in  1901,  has  been  much  used  in  adjusting 
birth-rates  and  death-rates.  It  is  as  follows: 


TABLE  38 
ENGLAND  AND  WALES   STANDARD   MILLION   OF  1901 


Age-group. 

Males. 

Females. 

Persons. 

(1) 

(2) 

(3) 

(4) 

0-5 

57,039 

57,223 

114,262 

5-9 

53,462 

53,747 

107,209 

10-14 

51,370 

51,365 

102,735 

15-19 

49.420 

50,376 

99,796 

20-24 

45,273 

50,673 

95,946 

25^34 

76,425 

85,154 

161,579 

35^4 

59,394 

63,455 

122,849 

45-54 

42,924 

46,298 

89,222 

55-64 

27,913 

31,828 

59,741 

65-74 

14,691 

18,389 

33,080 

75- 

5,632 

7,949 

13,581 

G.  H.  Knibbs  and  C.  H.  Wickens,1  statisticians  of  the 
Commonwealth  of  Australia  have  worked  out  in  a  very 
elaborate  way  the  probable  normal  age  distribution  of  the 
people  of  Europe  for  the  year  1900  or  thereabouts.  Eleven 
countries  are  considered.  The  results  were  as  follows: 

1  The  Determination  and  Uses  of  Population  Norms  representing 
the  Constitution  of  Populations  according  to  Age  and  Sex,  and  accord- 
ing to  Age  only,  Transactions,  15th  International  Congress  on  Hygiene 
and  Demography,  Vol.  VI,  p.  352. 


182 


POPULATION 


TABLE  39 

PER  CENT  OF  POPULATION  AT  EACH  AGE 
(Eleven  Countries  of  Europe) 


Age. 

Per 
cent. 

Age. 

Per 
cent. 

Age. 

Per 
cent. 

Age. 

Per 
cent. 

Age. 

Per 
cent. 

(1) 

(2) 

(1) 

(2) 

(1) 

(2) 

(i) 

(2) 

(1) 

(2) 

0 

2.46 

19 

1.90 

38 

1.25 

57 

0.67 

76 

0.20 

1 

2.43 

20 

.86 

39 

1.21 

58 

0.64 

77 

0.18 

2 

2.41 

21 

.83 

40 

1.18 

59 

0.62 

78 

0.16 

3 

2.38 

22 

.80 

41 

.15 

60 

0.59 

79 

0.13 

4 

2.35 

23 

.76 

42 

.11 

61 

0.57 

80 

0.11 

5 

2.33 

24 

.73 

43 

.08 

62 

0.54 

81 

0.10 

6 

2.30 

25 

.69 

44 

.05 

63 

0.51 

82 

0.08 

7 

2.27 

26 

.66 

45 

.02 

64 

0.49 

83 

0.07 

8 

2.24 

27 

.62 

46 

0.99 

65 

0.46 

84 

0.05 

9 

2.21 

28 

.59 

47 

0.96 

'66 

0.44 

85 

0.04 

10 

2.19 

29 

.56 

48 

0.93 

67 

0.42 

86 

0.03 

11 

2.15 

30 

.52 

49 

0.89 

68 

0.39 

87 

0.02 

12 

2.12 

31 

.49 

50 

0.86 

69 

0.37 

88 

0.02 

13 

2.09 

32 

1.45 

51 

0.84 

70 

0.34 

89 

0.01 

14 

2.06 

33 

1.41 

52 

0.81 

71 

0.32 

90 

15 

2.03 

34 

1.38 

53 

0.78 

72 

0.29 

91 

16 

2.00 

35 

1.35 

54 

0.75 

73 

0.27 

92 

0.02 

17 

1.96 

36 

1.31 

55 

0.73 

74 

0.24 

93 

18 

1.93 

37 

1.28 

56 

0.70 

75 

0.22 

94 

All 

ages 

100.0 

Age  distribution  of  the  population  of  the  United  States.  - 

On  account  of  the  heterogeneous  character  of  the  people 
of  the  United  States,  due  to  immigration  and  to  internal 
migrations,  we  find  that  states  and  cities  vary  widely  in  the 
age  composition  of  their  inhabitants.  In  the  older  parts  of 
the  country  we  find  a  more  normal  age  distribution  of  the 
people,  one  that  approaches  that  of  Sweden  and  Switzerland, 
but  in  the  newer  sections,  especially  in  the  west,  we  find  an 
abnormally  large  number  of  persons  of  middle-age.  This  is 
also  true  of  cities  to  which  persons  of  middle-age  are  drawn. 
On  the  other  hand  the  rural  districts  are  relatively  low  in 
the  middle-age  groups.  There  are  also  important  differences 


AGE  DISTRIBUTION 

MALES  FEMALES 


10        8         6         4         20 


FIG.  42.  —  Distribution  of  Population  by  Age  and  Sex,  United 
States,  1910, 


184 


POPULATION 


between  native  whites,  foreign  born  whites  and  negroes; 
and  between  males  and  females.  The  student  is  urged  to 
study  in  the  census  reports  these  differences  among  differ- 
ent classes  of  populations  and  in  different  sections  of  the 
country. 

The  following  table  shows  the  percentages  of  total  popula- 
tion in  1910  arranged  by  years: 


TABLE  40 

PER  CENT  OF  TOTAL  POPULATION,  BY  SINGLE  YEARS,  1910 
(United  States) 


Age 

0 

10 

20 

30 

40 

50 

60 

70 

80 

90 

0 

2.4 

2.0 

2.0 

2.0 

1.7 

1.2 

0.7 

0.4 

1 

2.1 

1.9 

1.9 

1.2 

0.9 

0.7 

0.4 

0.2 

2 

2.4 

2.1 

2.0 

1.6 

1.2 

0.9 

0.5 

0.2 

0.3 

* 

3 

2.3 

1.9 

1.9 

1.4 

1.0 

0.7 

0.4 

0.2 

4 

2.3 

2.0 

1.9 

1.4 

0.9 

0.7 

0.4 

0.2 

5 

2.2 

1.9 

2.0 

.7 

1.2 

0.7 

0.5 

0.2 

6 

2.2 

2.0 

1.8 

.4 

0.9 

0.7 

0.3 

0.2 

7 

2.1 

1.9 

1.7 

.2 

0.9 

0.5 

0.3 

0.1 

0.1 

t 

8 

2.1 

2.1 

1.9 

.5 

1.0 

0.6 

0.3 

0.1 

9 

2.0 

1.9 

1.5 

.2 

0.9 

0.5 

0.3 

0.1 

Less  than  0.1%. 


t  Age  unknown  =  0.2% 


The  concentrations  around  the  years  ending  in  0  and  5 
should  be  noticed.  The  differences  between  the  percentages 
for  males  and  females  in  the  whole  population  are  relatively 
slight. 

EXERCISES  AND    QUESTIONS 

1.  What  were  the  points  in  the  Washington  controversy  in  regard  to 
death-rates  and  population?      [See  Am.  J.  P.  H.,  Apr.,  1917,  June, 
1917,  Feb.,  1918.] 

2.  From  the  data  given  in  Table  3,  13th  Census,  Population,  Vol.  I., 
p.  24,  estimate  by  three  methods  the  probable  population  of  the  United 
States  in  1950. 


EXERCISES  AND  QUESTIONS 


185 


3.  What  was  the  average  annual  percentage  rate  of  increase  of  the 
population  of  the  United  States  between  1790  and  1800,  assuming  a 
geometrical  rate  of  increase?      Between  1900  and  1910? 

4.  Under  what  temperature  conditions  do  the  people  of  the  United 
States  live?     (See  llth  Census,  page  ix.) 

6.   Under  what  rainfall  conditions  do  the  people  of  the  United  States 
live?     (See  llth  Census,  page  ix.) 

6.  From  data  given  on  page  314  of  the  13th  Census,  Population, 
Vol.  I,  make  a  table  giving  the  age  distribution  by  single  years  of  the 
entire  population  of  the  United  States,  the  native  white  of  native 
parentage  and  the  foreign  born  white.. 

7.  Make  a  plot  of  the  last  tv{O. 

8.  Assuming  the  age  distribution  of  the  United  States  native  white 
population  of  native  parentage  (both  sexes)  as  given  below,  find  by 
graphical  methods  the  age  distribution  as  indicated. 


Given 

Wanted 

Age 

Per  cent 

Age 

Per  cent 

6HI 

13.2 

(M 

? 

5-9 

11.8 

5-14 

? 

10-29 

21.1 

15-24 

? 

20-29 

17.7 

25-34 

? 

30-39 

13.1 

35-44 

? 

40-49 

9.2 

45-64 

? 

50-59 

6.9 

65-84 

? 

60-69 

4.4 

70-79 

2.1 

80-89 

0.5 

Check  the  result  by  computation  from  figures  given  in  previous 
problems. 

9.  Look  up  the  "  Incremental  Increase  Method"  of  estimating  future 
populations.     (Jour.  Am.  Water  Works  Asso.,  March,  1915.) 

10.  What  is  meant  by  the  "Center  of  Population?"     Where  was 
the  centre  of  population  in  the  United  States  in  1790?     In  1910?     [U.  S. 
Census,  1910,  Population,  Vol.  I,  p.  45.] 

11.  What  is  the  "median  point  "  ? 

12.  Which  states  have  the  largest  per  cents  of  urban  population? 

13.  Describe  Moore's  ''  Expectancy  Curve,"  for  estimating  future 
populations.     (Engineering  News,  Nov.  2,  1916,  p.  844.) 


CHAPTER  VI 

GENERAL  DEATH-RATES,  BIRTH-RATES  AND  MAR- 
RIAGE-RATES 

Gross  death-rates  (general  death-rates.)  —  Stated  sim- 
ply, the  death-rate  is  the  rate  at  which  a  population  dies. 
It  is  the  ratio  between  the  number  of  persons  who  die  in  a 
given  interval  of  time  and  the  median  number  of  persons 
alive  during  the  interval.  Unless  otherwise  specified  the 
interval  of  time  is  considered  to  be  one  year.  For  the  sake 
of  comparison  the  ratio  mentioned  is  reduced  to  the  basis 
of  some  round  number  of  population,  generally  1000.  Not 
until  such  reduction  is  made  may  we  consider  this  ratio  as 
a  "  rate." 

The  computation  is,  of  course,  very  simple.  If  in  the 
year  1917  the  number  of  deaths  in  a  given  city  was  5710 
and  the  population  on  July  1  of  that  year  was  390,000,  then 
the  death-rate  was: 

5710  -r-  390,000,  or  14.6  for  each  thousand. 

The  death-rate  for  1917  was  therefore  14.6.  We  sometimes 
call  this  the  ^  general  "  death-rate  because- it  refers  to  the 
general  population.  Sometimes  it  is  called  the  "  crude  " 
death-rate  to  distinguish  it  from  rates  corrected  and  ad- 
justed in  various  ways.  Or  it  may  be  called  the  "  annual  " 
death-rate.  This  is  unnecessary,  however,  as  death-rates 
are  always  assumed  to  refer  to  a  year  as  the  basis  unless 
stated  to  the  contrary.  Perhaps  the  best  term  of  all  would 
be  the  "  Gross  death-rate,"  but  this  term  is  not  as  common. 

186 


PRECISION  OF   DEATH-RATES  187 

Death-rates  may  be  based  on  10,000  or  100,000  or 
1,000,000  of  population,  but  1000  is  the  common  base  for  all 
general  rates.  The  higher  numbers,  however,  are  often 
used  for  special  rates,  as  described  in  the  next  chapter. 

The  method  of  estimating  mid-year  population  was  fully 
described  in  the  preceding  chapter. 

Precision  of  death-rates.  —  The  accuracy  of  a  death- 
rate  depends  upon  the  accuracy  of  the  number  of  deaths 
and  the  correctness  of  the  estimated  population.  One  or 
both  of  these  may  be  in  error.  Only  in  a  census  year  can  the 
death-rate  be  computed  from  actual  facts,  because  only  in 
a  census  year  is  the  population  known  by  actual  count. 
In  other  years,  the  population  is  estimated,  and  hence  the 
death-rate  based  upon  it  must  also  be  regarded  as  an 
estimate.  Incorrect  estimates  of  population  obviously  must 
produce  incorrect  death-rates.  If  this  fact  be  kept  in  im'nd 
it  will  prevent  one  from  drawing  unwarranted  conclusions 
in  comparing  rates  which  differ  from  each  other  by  small 
amounts. 

It  is  quite  common  to  see  the  gross  death-rate,  referred  to 
1000  persons  as  a  basis,  expressed  to  the  second  place  of 
decimals.  This  is  warranted  in  the  case  of  large  popula- 
tions for  then  the  figures  in  the  second  decimal  place  have 
a  significant  value.  It  -is  not  warranted  for  small  popu- 
lations. This,  it  will  be  remembered,  was  discussed  in 
Chapter  II,  but  the  following  figures  will  further  illustrate 
the  point. 

In  A,  with  a  population  of  1000,  the  number  of  deaths 
was  16  and,  of  course,  the  death-rate  was  16.  An  error  of 
one  death,  the  smallest  possible  error,  would  have  made  the 
deaths  17  (or  15).  In  B,  with  a  population  of  10,000,  an 
error  of  one  death  would  have  changed  the  rate  from  16.0 
to  16.1;  in  C,  population  100,000,  from  16.00  to  16.01,  and 
in  D,  population  1,000,000,  from  16.000  to  16.001.  In  a 


188          DEATH-,   BIRTH-  AND   MARRIAGE-RATES 


TABLE  41 
PRECISION  OF  DEATH-RATES 


City. 

Population. 

Number  of  deaths. 

Death-rate. 

(1) 

(2) 

(3) 

(4) 

A 

I              1,000 
I              1,000 

16 
17 

16.00 
17.00 

B 

(            10,000 
i            10,000 

160 
161 

16.00 
16.10 

C 

j           100,000 
\           100,000 

1,600 
1,601 

16.00 
16.01 

D 

(        1,000,000 
\        1,000,000 

16,000 
16,001 

16.00 
16.001 

city  of  less  than  10,000  population  it  would  obviously  be 
unreasonable  to  use  two  decimal  places. 

Similarly  the  following  figures  show  the  differences  in 
population  required  to  change  the  death-rate  from  16.00 
to  16.10  in  cities  of  different  size,  the  actual  numbers  of 
deaths  remaining  the  same. 

TABLE  42 
PRECISION  OF  DEATH-RATES 


City. 

Death-rate. 

Number  of  deaths. 

Population. 

Difference  in 
population. 

(D 

(2) 

(3.) 

(4) 

(5) 

A 

j        16.00 
I       16.10 

16 
16 

1,000     ) 
994     f 

6 

B 

j        16.00 
1        16.10 

160 
160 

10,000     ) 
9,938     J 

62 

C 

f        16.00 
1        16.10 

1,600 
1,600 

100,000     I 
99,378     J 

621 

D 

f        16.00 
I        16.10 

16,000 
16,000 

1,000,000     ( 
993,789     j 

6211 

CORRECTED   DEATH-RATES 


189 


It  will  be  noticed  that  in  all  cases  the  percentage  differ- 
ence in  population  is  the  same,  i.e.,  0.62  per  cent.  This 
percentage  varies^  according  to  the  death-rate.  To  alter 
the  death-rate  from  12.00  to  12.10,  for  example,  if  the  num- 
ber of  deaths  remained  the  same,  would  require  a  change 
of  population  of  0.83  per  cent.  The  following  figures  show 
the  percentage  change  in  population  required  to  alter 
the  death-rate  by  0.10  per  1000  from  certain  given  death- 
rates. 

TABLE  43 


Change  of  rate  from 

Percentage 
change  of 

population. 

(1) 

(2) 

20.  00  to  20.  10 

0.50 

19.  00  to  19.  10 

0.52 

18.  00  to  18.  10 

0.55 

17.  00  to  17.10 

0.58 

16.  00  to  16.10 

0.62 

15.  00  to  15.10 

0.66 

14.  00  to  14.10 

0.71 

13.  00  to  13.10 

0.76 

12.  00  to  12.  10 

0.83 

11.  00  to  11.  10 

0.90 

10.  00  to  10.  10 

0.99 

As  a  rough  and  ready  rule  we  may  therefore  decide  that 
for  places  smaller  than  1000  the  death-rate  shall  be  stated 
in  whole  numbers;  for  places  between  1000  and  100,000 
one  decimal  shall  be  used;  for  places  above  100,000  two 
decimal  places  shall  be  used. 

Corrected  death-rates.  —  What  shall  be  taken  as  the 
number  of  deaths  in  a  community?  Shall  non-residents 
who  die  within  the  geographical  limits  be  included?  Shall 
residents  who  die  away  from  home  be  referred  back  to  the 
place  where  they  live?  In  other  words  shall  the  place  for 
which  the  death-rate  is  computed  be  considered  as  a  geo- 


190          DEATH-,   BIRTH-  AND   MARRIAGE-RATES 

graphical  area  or  as  a  community  of  persons?  The  answer 
must  depend  upon  the  use  which  is  to  be  made  of  the  facts. 

The  Bureau  of  the  Census,  looking  at  the  matter  in  a 
broad  way,  takes  the  geographical  point  of  view.  It  can 
hardly  do  otherwise.  By  recording  deaths  in  the  place 
where  the  deaths  actually  occur  there  is  far  less  danger  that 
all  deaths  will  not  be  recorded  and  that  no  death  will  be 
counted  twice  than  if  a  process  of  distribution  by  actual 
residence  were  attempted.  It  may  be  laid  down  as  a  general 
rule  that  in  computing  gross  death-rates  all  deaths  within 
the  defined  area  shall  be  included  and  no  others;  that  is, 
gross  death-rates  shall  have  a  geographical  basis. 

This  does  not  prevent  the  making  of  corrections  to  allow 
for  local  conditions.  Often  such  corrections  are  desirable. 
If  a  hospital  is  located  in  a  suburban  town  near  a  large  city 
the  deaths  in  that  hospital  should  be  included  in  the  gen- 
eral death-rate  of  the  town;  but  this  figure  could  not  be 
taken  as  an  index  of  the  hygienic  or  sanitary  condition  of 
the  town.  For  such  a  purpose  another  rate  —  a  corrected 
rate  —  should  be  computed,  leaving  out  the  hospital  deaths. 
This  might  be  called  the  local  death-rate.  This  rate  should 
not  be  used  in  place  of  the  gross  death-rate,  but  in  addition 
to  it. 

If,  besides  the  omission  of  non-resident  deaths  in  insti- 
tutions, the  attempt  is  made  to  find  and  include  the  deaths 
of  residents  who  have  died  away  from  home  we  might  call 
the  result  the  "  resident  death-rate." 

The  gross  death-rate,  or  general  rate,  is  best  for  pur- 
poses of  national  or  state  record.  The  local  rate  is  best  for 
environmental  studies.  The  resident  rate  is  useful  for 
social  and  political  studies. 

In  New  York  city  the  health  department  publishes  a 
general  death-rate  and  also  a  "  corrected  "  death-rate  in 
which  the  deaths  are  redistributed  among  the  five  boroughs 


CORRECTED  DEATH-RATES 


191 


on  the  basis  of  residence.  This  is  because  so  many  persons 
residing  in  one  borough  are  taken  to  hospitals  in  other 
boroughs.  In  some  cases  this  makes  an  important  differ- 
ence. For  the  week  ending  Mar.  23,  1918,  the  death- 
rates  for  the  five  boroughs  were  as  follows: 

TABLE  44 
DEATH-RATES  IN  NEW  YORK  CITY 


Borough. 

General  death- 
rate. 

Resident  death- 
rate. 

-       (1) 

(2) 

(3) 

Manhattan 

20.32 

20.30 

Bronx 

20.20 

17.68 

Brooklyn 

18.98 

20.04 

Queens 

20.71 

20.98 

Richmond 

25.13 

18.98 

On  the  basis  of  the  gross  death-rate  Richmond  is  seen 
to  have  a  death-rate  much  higher  than  Manhattan,  but 
its  resident,  or  "  corrected,"  rate  is  lower  than  that  of 
Manhattan. 

At  the  end  of  a  year  a  preliminary  death-rate  is  often 
computed  and  published.  Afterwards  delayed  reports  of 
deaths  are  received  and  this  necessitates  a  correction.  The 
term  "  corrected  "  death-rate  is  sometimes  applied  to  the 
new  result.  This  of  course  is  a  proper  use  of  the  adjective, 
but  a  better  term  would  be  "final." 

The  term  "  corrected  death-rate  "  has  been  used  by 
some  writers  as  synonymous  with  the  "  standardized  death- 
rate,"  described  on  page  240.  This  use  of  the  term  is 
unfortunate  and  should  be  avoided. 

Properly  the  word  "  corrected  "  should  be  applied  only 
to  death-rates  in  ..which  changes  are  made  in  the  number  of 
deaths. 


192          DEATH-    BIRTH-  AND   MARRIAGE-RATES 

Revised  death-rates.  —  Inasmuch  as  death-rates  are 
based  on  estimated  populations  in  post-censal  years,  and  as 
these  estimates  are  usually  less  accurate  than  intercensal 
estimates,  it  is  always  wise  after  each  new  census  to  re- 
compute the  death-rates  for  the  preceding  intercensal  years 
if  it  is  found  that  the  new  census  is  different  from  the 
estimated  population.  Sometimes  the  resulting  changes 
are  slight,  but  they  may  be  considerable.  The  rates  based 
on  these  revised  estimates  of  population  should  be  called 
"revised  death-rates." 

Variations  in  death-rates  in  places  of  different  size.  — 
Wide  fluctuations  in  the  general  death-rates  from  year  to 
year  are  to  be  expected  in  small  places.  Having  a  small 
population  a  change  of  one  death  in  a  year  may  consider- 
ably alter  the  rate.  In  larger  populations  the  fluctuations 
are  less  marked.  This  is  well  illustrated  by  the  death- 
rates  of  three  places  in  Massachusetts,  —  Boston  (popu- 
lation 686,092  in  1910),  Springfield  (88,926)  and  Yarmouth 
(1420).  Fig.  43  shows  that  the  death-rate  for  Boston 
changed  slowly,  that  of  Springfield,  althbugh  lower,  fluc- 
tuated more,  while  that  of  Yarmouth  varied  through  wide 
limits. 

This  very  well  illustrates  what  is  sometimes  called  the 
principle  of  large  numbers. 

Errors  in  published  death-rates.  —  It  is  necessary  to  use 
published  death-rates  and  birth-rates  with  great  caution. 
The  old  reports  especially  contain  many  unsuspected  errors. 
For  example,  it  was  not  at  all  uncommon  ten  or  twenty  years 
ago  for  the  population  of  one  census  to  be  used  year  after  year 
as  the  basis  of  death-rates,  or  until  a  new  census  was  taken ; 
that  is,  no  intercensal  estimates  were  made.  Even  the 
registration  reports  of  Massachusetts  are  full  of  inconsist- 
encies and  cases  of  disagreements.  In  the  following  table 
the  general  death-rates  are  given  in  the  second  column  as 


VARIATION  IN  DEATH-RATES 


193 


15 


1905   1906   1907    1908   1909    1910   1911    1912   1913   1914 


FIG.  43.  —  Comparison  of  Death-rates  in  a  Large  City,  a  City  of 
Moderate  Size  and  a  Small  Town. 


194         DEATH-,  BIRTH-  AND  MARRIAGE-RATES 


they  appeared  originally  in  successive  annual  reports.  In 
the  third  column  the  rates  for  the  same  "years  are  given  as 
published  in  the  annual  report  for  1915,  the  rates  having 
been  recomputed. 

TABLE  45 
DEATH-RATES  IN  MASSACHUSETTS 


Year. 

As  given 
originally  in 
successive 
annual  reports. 

As  given  in 
report  of  1915 
(recomputed). 

(1) 

(2) 

(3) 

1905 

16.8 

16.7 

1906 

16.9 

16.4 

1907 

18.1      - 

17.2 

1908 

17.2 

16.0 

1909 

17.0 

15.5 

1910 

16.2 

16.1 

1911 

15.8 

15.8 

1912 

15.6 

14.9 

1913 

15.9 

14.9 

1914 

14.5 

14.5 

Rates  for  short  periods.  —  The  general  death-rate  is 
always  computed  on  the  basis  of  a  year. 

Strictly  speaking  the  monthly  death-rate  would  be  the 
number  of  deaths  occurring  in  the  month  divided  by  the 
estimated  population  for  the  middle  of  the  month;  and  the 
weekly  death-rate  would  be  the  number  of  deaths  in  a  week 
divided  by  the  estimated  Wednesday  population  for  that 
week.  This  practice  would  reduce  population  estimates  to 
an  absurd  degree  of  precision.  The  months  moreover  do 
not  all  have  the  same  number  of  days.  On  account  of  the 
varying  estimates  of  population  the  sum  of  the  monthly 
rates  would  not  equal  the  annual  rates. 

It  is  much  better  for  many  reasons  to  reduce  all  rates 
for  short  periods  to  the  basis  of  a  year,  and  to  use  the  popu- 


RELATIONS  BETWEEN  BIRTH-  AND  DEATH-RATES      195 

lation  estimated  for  July  1  for  all  months  and  weeks  of  the 
same  year.  Account  must  be  taken,  too,  of  the  varying 
length  of  the  months,  and  of  the  fact  that  a  year  is  not 
exactly  fifty-two  weeks. 

To  find  the  death-rate  for  January  we  therefore  multiply 
the  number  of  deaths  in  January  by  Vi5,  and  divide  by  the 
estimated  population  for  July  1.  For  the  months  of  thirty 
days  the  multiplier  is  -\V;  for  February  it  is  tyf-  in  ordi- 
nary years,  and  Vs1  m  leaP  years. 

To  find  the  death-rate  for  any  week  in  the  year  we  mul- 
tiply the  number  of  deaths  in  the  week  by  -f A  and  divide 
by  the  population  estimated  for  July  1st. 

Birth-rates.  —  Birth-rates  are  computed  in  the  same  way 
as  death-rates.  We  may  have  general  rates,  local  rates, 
and  resident  rates;  preliminary  rates  and  final  rates;  cor- 
rected rates  and  revised  rates.  Weekly  and  monthly  rates 
are  reduced  to  a  yearly  basis. 

One  thing  should  be  always  remembered.  If  a  child  is 
born  dead,  that  is  if  it  is  a  "  still-birth,"  it  is  not  consid- 
ered by  statisticians  as  a  birth.  Births  include  only  living 
births.  Still-births  are  placed  in  a  class  by  themselves.  In 
some  places,  still-births  have  been  included  with  the  living 
births,  and  in  comparing  old  birth-rates  with  present  rates 
this  must  be  kept  in  mind.  It  must  be  remembered  also 
that  birth  registration  is  less  complete  than  the  registration 
of  deaths. 

Relations  between  birth-rates  and  death-rates.  —  The 
relations  which  exist  between  general  birth-rates  and  gen- 
eral death-rates  are  very  complicated.  It  is  easy  to  say  that 
because  of  a  naturally  high  infant  mortality,  which  until 
recently  has  seldom  been  less  than  10  per  cent  and  which  in 
some  countries  is  more  than  25  per  cent,  the  birth  of  many 
children  means  many  deaths  and  hence  a  high  birth-rate 
means  a  high  death-rate.  To  a  certain  extent  this  is  true. 


196         DEATH-,   BIRTH-  AND  MARRIAGE-RATES 

It  is  true  for  a  sudden  increase  in  the  birth-rate  and  its 
effect  may  last  for  five  or  ten  years  if  the  high  birth-rate 
keeps  up.  But  a  high  birth-rate  adds  to  the  population, 
and  this  increases  the  denominator  of  the  birth-rate. 
Also  most  of  the  babies  will  within  a  few  years  become 
children  and  enter  age  groups  where  the  specific  death-rates 
are  low.  If  a  high  birth-rate  is  long  continued  it  may  actually 
reduce  the  general  death-rate.  Fifty  or  sixty  years  after  a 
high  birth-rate  there  should  be  an  excess  of  persons  living 
within  the  advanced  age  groups  when  the  specific  death- 
rates  are  high  and  rapidly  increasing. 

Instead  of  becoming  confused  by  trying  to  think  out 
these  puzzling  relations,  and  especially  so  because  wars  and 
migrations  upset  all  such  reasonings,  it  is  better  to  regard 
the  birth-rate  as  something  which  together  with  deaths  and 
migrations  controls  the  age  composition  of  the  people. 
Conversely  the  age  composition  of  the  people  influences 
both  the  given  birth-rate  and  the  general  death-rate. 
One  cannot  think  clearly  on  this  subject  without  cutting 
loose  from  general  rates  and  studying  specific  rates  both 
for  births  and  deaths. 

Fecundity.  —  From  a  social  standpoint  the  birth-rates 
computed  in  the  usual  way  give  an  inadequate  idea  of  some 
of  the  most  important  matters  concerning  the  increase  of 
population.  They  are  ratios  between  births  and  total 
populations,  and  not  all  of  the  population  included  are 
child  producers.  If  we  are  to  follow  the  statistical  prin- 
ciple of  comparing  things  which  are  logically  comparable 
we  shall  compute  other  ratios,  that  between  births  and 
women  of  child  bearing  age  and  that  between  births  and 
married  women  of  child  bearing  age,  and  we  shall  separate 
legitimate  from  illegitmate  births,  and  take  into  account 
still  births,  though  always  keeping  them  separate  from 
living,  or  true  statistical  births. 


FECUNDITY  197 

What  are  the  chief  factors  which  control  the  number  of 
children  born?  The  number  of  marriages;  the  effective 
duration  of  these  marriages,  that  is  the  number  of  years  be- 
tween the  age  of  the  bride  at  marriage  and  the  natural  age 
when  child-bearing  ceases;  and  the  frequency  with  which 
conception  occurs.  The  number  of  marriages  depends  up- 
on the  age  and  sex  composition  of  the  population  and  upon 
economic  and  social  conditions.  The  effective  duration  of 
marriage  depends  upon  the  age  at  marriage,  especially 
the  age  of  the  bride.  Obviously  if  marriage  occurs  late  in 
life  the  effective  duration  of  marriage  is  shortened.  The 
frequency  of  conception  depends  to  some  extent  upon  the 
infant  mortality  as,  a  shortening  of  the  period  of  suckling 
reduces  the  child-bearing  interval;  but  to  a  considerable 
extent  this  is  a  matter  which  is,  or  may  be,  controlled  by 
the  husband  and  wife.  The  number  of  still  births  also  has 
an  influence  on  the  intervals  between  living  children. 

Korosi l  and  others  have  attempted  to  compute  tables  of 
natality,  similar  to  the  life  tables  described  in  Chapter  XIV. 
Statistics  for  Budapest  indicated  that  the  age  of  maximum 
fecundity  for  females  reached  its  maximum  between  the 
eighteenth  and  nineteenth  years,  falling  steadily  to  age 
fifty  when  it  practically  ceased.  Males  attain  their  maxi- 
mum fecundity  at  the  age  of  about  twenty-five,  after  which 
there  is  a  steady  decline  to  age  sixty-five  or  thereabouts. 
It  is  understood  that  these  figures  are  not  physiological 
limits  necessarily,  but  include  social  and  economical  con- 
siderations. Late  marriages  therefore  reduce  the  number 
of  resulting  children.  Combinations  of  brides  and  grooms 
of  different  ages  results  in  different  probabilities  of  births. 
The  following  figures  given  by  Korosi  illustrate  this.  The 
percentages  refer  to  the  probability  of  a  birth  occurring  in 
a  year. 

1  1899,  Newsholme,  Vital  Statistics,  p.  667. 


198          DEATH-,   BIRTH-  AND   MARRIAGE-RATES 


TABLE  46 
RELATION  OF  AGE  TO  FECUNDITY 


Fecundity  of  mothers. 

Fecundity  of  fathers. 

Age  of 
father. 

Age  of  mother. 

Age  of 
mother. 

Age  of  father. 

25  yrs. 

30  yrs. 

35  yrs. 

25  yrs. 

35  yrs. 

45  yrs. 

55  yrs. 

(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

(7) 

(7) 

(9) 

25-29 
30-34 
35-39 
40-44 
45-49 
50-54 

Per 

cent 

36 
31 
27 

Per 

cent 

25 
24 
22 
17 
14 

Per 

cent 

21 
20 
19 
14 
11 
11 

20 
20-24 
25-29 
30-34 
35-39 
40-44 

Per 
cent 

49 
43 
31 
33 

Per 

cent 

Per 

cent 

Per 

cent 

31 

27 
24 
19 

7 

16 
18 
14 
12 
6 



8 
7 
3 

Nationalities  differ  considerably  in  the  number  of  chil- 
dren per  marriage.  For  example,  in  Russia,  the  number 
of  children  per  marriage  in  1894  averaged  as  high  as  5.7, 
while  in  France  it  was  only  3.0.  During  recent  years  in 
most  countries  the  birth-rates  have  fallen  considerably.  In 
studying  this  subject  in  its  social  relations,  these  natural 
conditions  of  fecundity  as  influenced  by  the  age  composi- 
tion of  the  people,  the  age  of  marriage  and  the  influence 
of  nationality  must  be  taken  into  account. 

Illegitimate  births.  —  Children  born  to  unmarried  women 
are  called  illegitimate.  In  computing  general  birth-rates 
they  are  included,  but  in  the  study  of  social  problems  they 
should  be  considered  by  themselves.  The  illegitimate  birth- 
rate is  the  ratio  between  illegitimate  births  and  the  total 
population  expressed  in  thousands.  The  percentage  of  ille- 
gitimacy is  sometimes  computed,  that  is  the  ratio  between 
illegitimate  and  total  births,  but  this  ratio  may  be  mislead- 
ing as  the  total  number  of  births  depends  on  the  marriage- 


ILLEGITIMATE  BIRTHS 


199 


rate,  which  fluctuates  more  or  less  according  to  economic 
conditions.  As  a  measure  of  morality  a  more  useful  ratio 
is  that  between  illegitimate  births  and  unmarried  women  of 
child-bearing  age.  It  is  just  as  important  to  consider  the 
age  and  sex  composition  of  a  population  in  studying  illegiti- 
mate births  as  in  studying  all  births. 

Newsholme  has  given  the  following  interesting  compari- 
sons between  two  sections  of  London,  Kensington,  an 
aristocratic  fashionable  district,  and  Whitechapel,  a  poor 
industrial  parish. 

TABLE  47 
BIRTH-RATES  IN  KENSINGTON  AND  WHITECHHAPEL,   1891 


Birth-rate. 

Legitimate. 

Illegitimate. 

Ken- 
sington. 

White- 
chapel. 

Excess 
in 
White- 
chapel. 

Ken- 
sington. 

White- 
chapel. 

Excess 
in 
White- 
chapel. 

(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

(7) 

A  Per  thousand  of  popula- 
tion . 

21.8 
61.6 
215.4 

39.9 
172.1 
328.3 

Per 
cent. 

83 
177 
53 

1.2 
3.4 

4.7 

1.3 

5.4 

11.4 

Per 
cent. 

6 
62 

136 

B  Per  thousand  of  women, 
aged  15-44  years  
C  Per  thousand  married 
women,  aged  15-44  years 
D  Per  thousand,   unmar- 
ried women,  aged  15-44 
years. 

We  see  from  this  table  that  on  the  basis  of  married 
women  of  child-bearing  age  the  birth-rate  in  the  industrial 
district  of  Whitechapel  was  only  53  per  cent  greater  than 
in  the  fashionable  district  of  Kensington.  On  the  basis,  of 
the  general  birth-rate  or  the  rate  computed  for  all  women 
of  child-bearing  age  the  difference  between  the  two  districts 


200         DEATH-,  BIRTH-  AND  MARRIAGE-RATES 

would  have  been  said  to  be  much  greater.  In  Kensington 
there  were  many  unmarried  servants.  The  illegitimate 
birth-rate  computed  on  the  basis  of  total  population  was 
only  6  per  cent  greater  in  Whitechapel  than  in  Kensington, 
but  on  the  t>asis  of  unmarried  women  of  child-bearing  age 
it  was  136  per  cent  greater.  This  is  an  excellent  example 
of  the  necessity  of  considering  specific  rates  in  the  study 
of  illegitimacy.  Fallacious  conclusions  in  regard  to  the 
relative  morality  of  different  nationalities,  of  urban  and 
rural  districts,  of  different  states  and  cities  have  resulted 
from  failure  to  take  the  proper  ratios  as  a  basis  ol 
study. 

Marriage-rates.  —  The  marriage-rate  is  found  by  dividing 
the  number  of  persons  married  in  a  year  by  the  estimatec 
mid-year  population,  expressed  in  thousands.  The  wed- 
ding-rate would  be  one-half  of  the  marriage-rate.  In  some 
places  this  wedding-rate  is  called  the  marriage-rate,  bu1 
this  is  not  according  to  present-day  practice.  To  prevent 
misunderstanding  it  is  a  good  plan  to  use  the  expressior 
"  persons  married  per  1000  population." 

Divorce-rates.  —  Similarly  the  divorce-rate  is  found  bj 
dividing  the  number  of  persons  divorced  in  a  year  by  the 
mid-year  population. 

Divorce  in  the  United  States  is  becoming  more  and  more 
important  as  a  social  problem.  The  conditions  are  dif- 
ferent in  different  states.  In  Massachusetts  the  data,  ob- 
tained originally  from  court  records,  are  published  in  the 
State  Registration  Report.  The  following  figures  are  froir 
the  report  of  1914. 

The  divorce-rate,  based  on  an  average  for  five  years  ol 
which  the  census  year  was  the  median,  has  increased  as 
follows. 


DIVORCE-RATES 


201 


TABLE  48 
DIVORCE-RATE,  MASSACHUSETTS 


Median 
year. 

Average  rate 
per  100,000 
population. 

Average  per 
100,000  of  mar- 
ried population. 

(1) 

(2) 

(3) 

1880 

30 

1890 

32 

86 

1900 

46 

123 

1905 

58 

153 

1910 

56 

146 

1914 

60 

156 

The  relative  number  of  divorces  granted  to  wives  is 
larger  than  the  number  granted  to  husbands.  At  present 
the  ratio  is  in  round  numbers  7:3. 

The  percentage  distribution  of  divorces  according  to 
cause  has  been  as  follows: 

TABLE   49 
CAUSES  OF  DIVORCE,  MASSACHUSETTS,   1860  to   1914 


Cause. 

Percentage. 

Granted  to 
husband. 

Granted  to 
wife. 

(1) 

(2) 

(3) 

Desertion                        

Per  cent. 
56.7 
34.8 

5.8 
1.5 
0.7 
0.2 
0.2 
i 

Per  cent. 

41.5 
14.8 
14.4 
19.8 
0.4 
4.1 
0.2 
4.2 
0.5 

Adultefy                      

Intoxication 

Cruel  find  abusive  treatment                               .  • 

Nullity  of  marriage                               

Extreme  cruelty                                  

Impotency                                       

Neclect  to  provide 

Imprisonment  

i    - 

Total                                     

100.0% 

ioa.o% 

1  Less  than  0.1  per  cent. 


202          DEATH-,   BIRTH-  AND   MARRIAGE-RATES 


About  three  out  of  every  four  applications  for  divorce  in 
Massachusetts  are  granted.  About  nine  out  of  ten  are  not 
contested. 

The  distribution  of  divorces  according  to  the  duration 
of  marriage  is  interesting.  In  1914  the  average  duration 
of  the  marriage  at  the  time  application  for  divorce  was 
made  10.9  years.  The  2963  applications  were  distributed 
as  follows: 

TABLE  50 
DURATION  OF  MARRIAGES  ENDING  IN  DIVORCE 


Duration  of 
marriage. 

Per  cent  of 
applications. 

(1) 

(2) 

0-  6  months 

0.7 

6-11        " 

1-4    years 
5-9      " 

27.4 
30.7 

10-19 

28.7 

20-29 

10.3 

30 
Total  

2.2 

100.0    . 

In  discussions  of  the  divorce  problem  comparison  is 
sometimes  made  between  marriage-rates  and  divorce-rates. 
This  is  not  a  logical  comparison.  Why?  The  student  must 
begin  to  answer  such  questions  as  this  on  the  basis  of  his  own 
reasoning. 

In  1910  in  Massachusetts  divorce  was  dissolving  each  year 
about  3  marriages  out  of  every  1000  in  existence,  or,  more 
exactly,  one  out  of  every  342;  in  1897  one  out  of  every 
580. 

The  U.  S.  Bureau  of  the  Census  has  estimated  the  prob- 
ability of  divorce l  as  not  less  than  1  in  16,  and  probably  1 
in  12.  This  figure  was  based  on  the  statistics  of  1900,  and 
1  Marriage  and  Divorce,  1867-1906,  Vol.  I,  pp.  23,  24. 


NATURAL  RATE  OF  INCREASE 


203 


means  that  one  marriage  in  every  16  would  probably  be  ended 
by  divorce  instead  of  continuing  until  "  death  do  us  part." 

This  general  figure  must  not  be  taken  too  seriously,  as  it 
includes  all  classes  of  people  living  under  many  different  con- 
ditions and  represents  past  rather  than  present  conditions. 

Divorce  statistics  ought  to  be  studied  specifically,  just  as 
much  as  births  and  deaths. 

Natural  rate  of  increase.  —  The  difference  between  the 
birth-rate  and  the  'death-rate  gives  the  natural  rate  of 
increase  (or  decrease)  in  population  per  1000  inhabitants. 
In  the  absence  of  immigration  and  emigration,  and  if  the 
data  are  correct,  the  excess  of  births  over  deaths  will  cor- 
respond with  the  increase  of  population  as  revealed  by  the 
census  counts.  This  may  be  illustrated  by  the  statistics  of 
Sweden  from  1750  to  1900. 

TABLE  51 
INCREASE  OF  POPULATION  IN    SWEDEN 


Per  1000  of  population  at  middle  of  period. 

Year. 

Population  at  end 
of  given  year 
(thousands). 

Increase  as  shown 
by  census. 

Excess  of  births 
over  deaths. 

Emigration  (com- 
puted from  last 
two  columns). 

(1) 

(2) 

(3) 

(4) 

(5) 

1750 

1781 

8.89 

8.89 

0.00 

1760 

1925 

'7.76 

8.43 

0.67 

1770 

2043 

5.92 

6.60 

0.68 

1780 

2118 

3.71 

4.14 

0.43 

1790 

2188 

3.22 

4.03 

0.81 

1800 

2347 

6.99 

7.96 

0.97 

1810 

2396 

2.04 

2.63 

0.59 

1820 

2584 

7.60 

7.52 

-0.08 

1830 

2888 

11.02 

11.00 

-0.02 

1840 

3139 

8.32 

8.69 

0.37 

1850 

3482 

10.39 

10.51 

0.12 

1860 

3860 

10.36 

11.10 

0.74 

1870 

4169 

7.57 

11.24 

3.67 

1880 

4566 

9.05 

12.21 

3.16 

1890 

4785 

4.69 

12.12 

7.43 

1900 

5136 

7.13 

10.78 

3.65 

204          DEATH-,   BIRTH-  AND   MARRIAGE-RATES 

The  figures  in  the  last  column  show  that  there  was  very 
little  emigration  before  1870,  but  that  since  then  the  losses 
by  emigration  have  been  considerable.  It  is  quite  likely, 
however,  that  some  of  the  early  birth-rates  were  not  as 
accurate  as  the  more  recent  ones. 

Comparison  of  general  rates.  —  The  object  of  computing 
gross  death-rates  is  to  enable  us  to  compare  the  general 
mortality  in  places  of  different  population  and  of  different 
years  in  the  same  place ;  and  yet,  as  will  be  demonstrated  in 
the  next  chapter,  such  comparisons  are  very  apt  to  be  mis- 
leading unless  the  percentage  composition  of  the  popu- 
lation remains  substantially  constant  in  all  the  places  and 
in  all  the  years  which  are  compared.  One  naturally  asks, 
"  Why,  if  such  is  the  case,  should  we  compute  it  at  all?  " 
The  answer  is  that  in  a  general,  and  crude  way  the  gross 
rate  does  show  differences  in  the  mortality  of  different 
places,  and  that  in  any  given  place  the  composition  of  the 
population  changes  slowly  from  year  to  year.  Large  differ- 
ences in  general  death-rates  may  be  significant,  but  small 
differences  are  usually  not  significant. 

What  is  true  of  general  death-rates  is  also  true  of  birth- 
rates and  marriage-rates.  Far  too  much  attention  in 
studies  of  vital  statistics  is  given  to  comparisons  of  general 
rates.  Such  comparisons  are  likely  to  be  superficial  and 
sterile  of  results.  Nevertheless  one  should  have  a  general 
appreciation  of  the  changes  which  have  taken  place  in 
birth-rates  and  death-rates  throughout  the  world  during 
the  last  fifty  years.  A  few  examples  will  be  given,  but 
the  reader  should  consult  more  extended  works  on  the 
subject  and  compile  for  himself  tables  of  rates  taken  from 
official  reports. 

Marriage-rates,  birth-rates  and  death-rates  in  Sweden. 

—  One  of  the  longest  records  of  birth-rates,  marriage-rates 

and  death-rates  is  that  of  Sweden.     Table  48  shows  these 


VITAL  STATISTICS  OF  SWEDEN 


205 


206         DEATH-,  BIRTH-  AND  MARRIAGE-RATES 

rates  from  1749  to  1900.  The  death-rates  and  birth-rates 
are  also  shown  in  Fig.  44.  It  will  be  seen  that  the  birth- 
rate has  had  a  general  downward  trend  for  a  long  time,  but 
especially  during  the  last  fifty  years.  The  death-rate  has 
fallen  more  than  the  birth-rate  so  that  the  natural  in- 
crease has  risen.  Of  course,  there  have  been  fluctuations 
and  some  very  abnormal  rates  will  be  found.  As  one  would 
naturally  expect  the  birth-rate  has  fluctuated  synchro- 
nously with  the  marriage-rate.  At  intervals  great  epi- 
demics have  occurred  which  carried  the  death-rate  far  above 
the  birth-rate.  As  a  statistical  series  this  diagram  is  de- 
serving of  careful  study.  The  dotted  line  shows  the  "  mov- 
ing average  "  referred  to  in  Chapter  II. 


MARRIAGE-,  BIRTH-  AND  DEATH-RATES,  SWEDEN     207 

TABLE  48 

MARRIAGE-RATES,  BIRTH-RATES,  AND  DEATH-RATES 
Sweden,  1749-1900  (After  Sundbarg) 


Year. 

Mar- 
riage- 
rate. 

Birth- 
rate. 

Death- 
rate. 

Natural 
in- 
crease. 

Year. 

Mar- 
riage- 
rate. 

Birth- 
rate. 

Death- 
rate. 

Natural 
increase. 

(1) 

(2) 

(3) 

(4) 

(5) 

(1) 

(2) 

(3) 

(4) 

(5) 

1749 

17.10 

33.82 

28.13 

5.69 

1750 

18.48 

36.40 

28.83 

9.57 

1780 

17.06 

35.70 

21.74 

13.96 

1751 

18.54 

38.63 

26.18 

12.45 

1781 

14.66 

33.46 

25.55 

7.91 

1752 

18.52 

35.91' 

27.34 

8.57 

1782 

15.36 

32.05 

27.26 

4.79 

1753 

17.42 

36.12 

24.03 

12.09 

1783 

15.98 

30.33 

28.11 

2.22 

1754 

18.90 

37.22 

26.33 

10.89 

1784 

14.96 

31.53 

29.75 

1.78 

1755 

18.32 

37.52 

27.38 

10.14 

1785 

15.64 

31.43 

28.30 

3.13 

1756 

17.00 

36.12 

27.66 

8.46 

1786 

16.04 

32.89 

25.94 

6.95 

1757 

15.94 

32.  6L 

29.92 

2.69 

1787 

15.90 

31.47 

23.95 

7.52 

1758 

16.14 

33.42 

32.37 

1.05 

1788 

15.78 

33.87 

26.68 

7.19 

1759 

19.50 

33.62 

26.27 

7.35 

1789 

15.86 

32.01 

33.13 

-1.12 

1760 

19.52 

35.70 

24.78 

10.92 

1790 

16.50 

30.48 

30.43 

0.05 

1761 

18.88 

34.82 

25.80 

9.02 

1791 

21.68 

32.63 

25.49 

7.14 

1762 

17.92 

35.08 

31.22 

3.86 

1792 

20.02 

36.58 

23.90 

12.68 

1763 

17.28 

34.98 

32.90 

2.08 

1793 

17.80 

34.39 

24.27 

10.12 

1764 

17.58 

34.70 

27.24 

7.46 

1794 

16.36 

33.79 

23.60 

10.19 

1765 

16.30 

33.41 

27.68 

5.73 

1795 

15.18 

32.04 

27.94 

4.10 

1766 

16.54 

35.36 

25.06 

10.30 

1796 

17.24 

34.68 

24.65 

10.03 

1767 

16.54 

35.36 

25.63 

9.73 

1797 

16.88 

34.77 

23.81 

10.96 

1768 

16.92 

33.61 

27.17 

6.44 

1798 

16.58 

33.68 

23.08 

10.60 

1769 

16.26 

33.06 

27.15 

5.91 

1799 

14.70 

32.02 

25.18 

6.84 

1770 

16.24 

32.98 

26.06 

6.92 

1800 

14.90 

28.72 

31.43 

0.9 

1771 

15.52 

32.24 

27.77 

4.47 

1801 

14.50 

30.04 

26.08 

3.96 

1772 

13.64 

28.89   37.41 

-8.52 

1802 

15.66 

31.72 

23.71 

8.01 

1773 

15.5V 

25.52!  52.45 

-26.93 

1803 

16.38 

31.36 

23.77 

7.59 

1774 

8.77 

34.45 

22.36 

12.09 

1804 

16.14 

31.90 

24.87 

7.03 

1775 

18.90 

35.63 

24.84 

10.79 

1805 

16.74 

31.73 

23.48 

8.25 

1776 

18.02 

32.92 

22.50 

10.42 

1806 

16.08 

30.75 

27.51 

3.24 

1777 

18.14 

33.03 

24.93 

8.12 

1807 

16.40 

31.16 

26,22 

5.94 

1778 

18.10 

34.82 

26.65 

8.17 

1808 

16.24 

30.39 

34.85 

5.54 

1779 

17.34 

36.70 

28.50 

8.20 

1809 

15.62 

26.67 

40.04 

13.37 

208 


DEATH-,   BIRTH-  AND   MARRIAGE-RATES 


TABLE  48 

MARRIAGE-RATES,  BIRTH-RATES,  AND  DEATH-RATES 
Sweden,  1749-1900  (After  Sundbarg) 


Year. 

Mar- 
riage- 
rate. 

Birth- 
rate. 

Death- 
rate. 

Natural 
in- 
crease. 

Year. 

Mar- 
riage- 
rate. 

Birth- 
rate. 

Death- 
rate. 

Natural 
increase. 

(1) 

(2) 

(3) 

(4) 

(5) 

(1) 

(2) 

(3) 

(4) 

(5) 

1810 

21.52 

32.95 

31.57 

1.38 

1840 

14.14 

31.43 

20.35 

11.08 

1811 

21.32 

35.30 

28.81 

6.49 

1841 

14.34 

30.33 

19.42 

10.91 

1812 

18.26 

33.57 

30.27 

3.30 

1842 

14.22 

31.65 

21.06 

10.59 

1813 

15.48 

29.74 

27.37 

2.37 

1843 

14.38 

30.78 

21.45 

9.33 

1814 

15.04 

31.19 

25.07 

6.12 

1844 

14.88 

32.15 

20.27 

11.88 

1815 

19.22 

34.77 

23.59 

11.18 

1845 

14.58 

31.45 

18.83 

12.62 

1816 

19.60 

35.32 

22.66 

12.66 

1846 

13.80 

29.94 

21.83 

8.11 

1817 

16.68 

33.40 

24.25 

9.15 

1847 

13.64 

29.58 

23.69 

5.89 

1818 

16.92 

33.83 

24.37 

9.46 

1848 

14.64 

30.33 

19.68 

10.65 

1819 

16.28 

32.99 

27.36 

5.63 

1849 

15.66 

32-84 

19.84 

13.00 

1820 

16.88 

32.97 

24.46 

8.51 

1850 

15.18 

31.89 

19.79 

12.10 

1821 

17.62 

35.44 

25.57 

9.87 

1851 

14.72 

31.74 

20.72 

11.02 

1822 

18.58 

35.88 

22.59 

13.29 

1852 

13.68 

30.69 

22.70 

7.99 

1823 

17.98 

36.83 

21.02 

15.81 

1853 

14.40 

31.37 

23.66 

7.71 

1824 

17.66 

34.56 

20.77 

13.79 

1854 

15.38 

33.50 

19.76 

13.74 

1825 

17.20 

36.49 

20.54 

15.95 

1855 

15.04 

31.75 

21.45 

10.30 

1826 

16.16 

34.84 

22.61 

12.23 

1856 

14.88 

31.47 

21.77 

9.70 

1827 

14.44 

31.30 

23.05 

8.25 

1857 

15.50 

32.43 

27.58 

4.85 

1828 

15.82 

33.61 

26.74 

6.87 

1858 

16.22 

34.77 

21.69 

13.08 

1829 

15.82 

34.85 

28.97 

5.88 

1859 

16.56 

34.99 

20.13 

14.86 

1830 

15.46 

32.91 

24.08 

8.83 

1860 

15.60 

34.83 

17.65 

17.18 

1831 

13.80 

30.49 

26.00 

4.49 

1861 

14.54 

32.57 

18.47 

14.10 

1832 

14.38 

30.86 

23.38 

7.48 

1862 

14.52 

33.38 

21.40 

11.98 

1833 

15.66 

34.11 

21.74 

12.37 

1863 

14.52 

33.62 

19.33 

14.29 

1834 

16.02 

33.74 

25.68 

8.06 

1864 

13.96 

33.61 

20.25 

13.36 

1835 

15.00 

32.67 

18.55 

14.12 

1865 

14.14 

32.81 

19.36 

13.45 

1836 

14.34 

31.84 

19.97 

11.87 

;  1866 

13.44 

33.11 

19.98 

13.13 

1837 

13.80 

30.84 

24.65 

6.19 

1867 

12.18 

30.83 

19.64 

11.19 

1838 

12.18 

29.37 

24.10 

5.27 

1868 

10.92 

27.47 

20.98 

6.49 

1839 

13.54 

29.49 

23.56 

5.93 

1869 

11.28 

28.25 

22.27 

5.98 

MARRIAGE-,  BIRTH-  AND  DEATH-RATES,  SWEDEN     209 


TABLE  48 

MARRIAGE-RATES,  BIRTH-RATES,  AND  DEATH-RATES 
Sweden,  1749-1900  (After  Sundbarg) 


Year. 

Mar- 
riage- 
rate. 

Birth- 
rate. 

Death- 
rate. 

Natural 
in- 
crease. 

Year. 

Mar- 
riage 
rate. 

Birth- 
rate. 

Death- 
rate. 

Natural 
increase. 

(1) 

(2) 

(3) 

(3) 

(5) 

(1) 

(2) 

(3) 

(4) 

(5) 

1870 

12.04 

28.78 

19.80 

8.98 

1871 

12.98 

30.42 

17.21 

13.21 

1872 

13.86 

30.04 

16.28 

13.76 

1873 

14.62 

30.80 

17.20 

13.60 

1874 

14.54 

30.85 

20.32 

10.53 

1875 

14.10 

31.17 

20.27 

10.90 

1876 

14.16 

30.84 

19.59 

11.25 

1877 

13.66 

31.07 

18.66 

12.41 

1878 

12.94 

29.83 

18.06 

11.77 

1879 

12.58 

30.52 

16.94 

13.58 

1880 

12.64 

29.36 

18.10 

11.26 

1881 

12.38 

29.07 

17.68 

11.39 

1882 

12.66 

29.35 

17.35 

12.00 

1883 

12.86 

28.94 

17.31 

11.63 

1884 

12.06 

30.01 

17.53 

12.48 

1885 

13.26 

29.44 

17.75 

11.69 

1886 

12.82 

29.76    16.61 

13.15 

1887 

12.50 

29.66 

16.13 

13.53 

1888 

11.84 

28.78 

15.99 

12.79 

1889 

11.98 

27.74 

15.99 

11.75 

1890 

11.98 

27.95 

17.12 

10.83 

1891 

11.66 

28.27 

16.81 

11.46 

1892 

11.38 

26.98 

17.88 

9.10 

1893 

11.30 

27.36 

16.83 

10.53 

1894 

11.48 

27.10 

16.38 

10.72 

1895 

11.74 

27.49 

15.19 

12.30 

1896 

11.90 

27.18 

15.64 

11.54 

1897 

12.12 

26.67 

15.35 

11.32 

1898 

12.28 

27.  11 

15.08 

12.03 

, 

1899 

12.48 

26.35 

17.65 

8.70 

1900 

12.30 

27.00 

16.84 

10.16 

210         DEATH-,  BIRTH-  AND  MARRIAGE-RATES 


Downward  trend  in  birth-rates  and  death-rates.  — 
For  nearly  half  a  century  there  has  been  a  general  down- 
ward trend  in  the  birth-rates  and  death-rates  of  almost  all 
civilized  countries.  There  is  space  here  for  only  a  few 
figures  which  represent  averages  for  quinquennial  periods. 
They  are  taken  from  the  reports  of  the  Registrar-General 
of  England. 

TABLE  49 

CHRONOLOGICAL  CHANGES  IN  VITAL  RATES 


Country. 

Quinquennial  averages. 

1881-5 

1886-90 

1891-5 

1896-00 

1901-5 

1906-10 

1911-15 

(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

(7) 

(8) 

Birth-rates. 


England  and  Wales 

33.5 

31.4 

30.5 

29.3 

28.1 

26.3 

23.6 

Germany 

37.0 

36.5 

'36.3 

36.0 

34.3 

32.7 

France 

24.7 

23.1 

22.3 

21.9 

21.2 

19.9 

Hungary 

44.6 

43.7 

41.7 

39.4 

37.2 

37.0 

Death-rates. 


England  and  Wales 

19.4 

18.9 

18.7 

17.7 

16.0 

14.7 

14.3 

Germany 

25.3 

24.4 

23.3 

21.2 

19.9 

17.5 

France 

22.2 

22.0 

22.3 

20.7 

19.6 

19.2 

Hungary 

33.1 

32.1 

31.8 

27.9 

26.2 

25.0 

.... 

Rates  of  natural  increase. 


England  and  Wales 

14.1 

12.5 

11.8 

11.6 

12.1 

11.6 

9.3 

Germany 

11.7 

12.1 

13.0 

14.8 

14.4 

15.2 

France 

2.5 

1.1 

0.0 

1.2 

1.6 

0.7 

Hungary 

11.5 

11.6 

9.9 

11.5 

11.0 

12.0 

.... 

In  most  countries  the  natural  rate  of  increase  tends  to 
lie  between  the  limits  of  8  and  14  per  1000,  i.e.,  between 
0.8  and  1.4  per  cent,  but  sometimes  it  runs  above  1.4  per 
cent  or  below  0.8  per  cent  per  year.  France  is  an  example  of 


VARIATIONS  DUE  TO  POPULATION  ESTIMATES     211 


an  extremely  low  rate  of  natural  increase.  In  Germany  both 
the  birth-rates  and  death-rates  have  been  higher  than  in 
England.  In  Hungary  both  rates  have  been  much  higher 
than  in  Germany,  yet  the  rate  of  natural  increase  has  been 
lower.  The  student  should  seek  to  explain  all  of  these  facts. 


18 

r 

3  16 
15 

^ 
?. 

\/ 

/ 

3,200,000j 
1 

3,000,0001" 
2,800,000 

X% 

^v 

,''cx- 
S 

*\ 

^ 
£Z£. 

*£2%f 
^ 

A 

\/ 

i 

18* 

17 
16 
15< 
n 

LO 
3,400,000 

3,200,000 
3,000,000 
2,800,000 

900                       1905                          199 

K^ 

5 

^ 

l\ 

J 

^ 
^ 

E 

"~~-*^^ 

j* 

/ 

B 

\Jf 

1900  1905  1910 

FIG.  45.  —  Estimated  Death-rates  and  Populations,  Massachu- 
setts, 1900-1910. 

Variations  due  to  population  estimates.  —  Some  of  the 
variations  in  the  general  death-rates  from  year  to  year  are 
due  to  the  use  of  incorrect  population  estimates.  The 
following  comparison  is  interesting. 

Fig.  45  shows  the  populations  and  death-rates  for  the  state 
of  Massachusetts  from  1900  to  1910,  based  on  the  following 
data:1 

1  Registration  Report,  1914,  p.  176. 


212          DEATH-,   BIRTH-  AND   MARRIAGE-RATES 


TABLE  50 
DEATH-RATES:    MASSACHUSETTS 


Year. 

Population. 

Deaths. 

Death-rates. 

(1) 

(2) 

(3) 

(4) 

1900 

2,806,346  (census) 

51,156 

18.2 

1901 

2,849,047 

48,275 

16.9 

1902 

2,889,386 

47,491 

16.4 

1903 

2,929,725 

49,054 

16.7 

1904 

2,970,064 

48,482 

16.3 

1905 

3,015,872  (census) 

50,486 

16.7 

1906 

3,089,029 

50,624 

16.4 

1907 

3,162,186 

54,234 

17.2 

1908 

3,235,343 

51,788 

16.0 

1909 

3,308,500 

51,236 

15.5 

1910 

3,380,151  (census) 

54,407 

16.1 

The  upper  diagram  shows  the  estimated  population  as 
a  uniform  change  from  1900  to  1905  and  again  from  1905  to 
1910.  The  death-rates  computed  from  the  actual  deaths 
and  estimated  populations  are  seen  to  vary  irregularly. 
But  suppose  we  assume  that  the  changes  in  death-rates 
between  1900  and  1905  and  1905  and  1910  are  uniform. 
Then  we  can  compute  the  changes  in  population  from 
these  estimated  rates  and  the  actual  deaths.  The  results 
are  shown  in  the  lower  diagram.  Do  these  irregular  fluc- 
tuations seem  to  be  reasonable? 

There  is  no  way  of  telling  exactly  how  much  of  the  in- 
crease or  decrease  in  the  general  death-rate  is  due  to  actual 
increase  in  mortality  and  how  much  to  error  in  the  esti- 
mated population.  Both  factors  are  involved. 

Birth-rates  and  death-rates  in  Massachusetts.  —  Fig. 
46  shows  the  annual  variations  in  birth-rates  and  death- 
rates  from  1850  to*L915.  The  stars  indicate  the  so-called 
panic  years,  or  years  of  business  depression.  The  tendency 
has  been  for  the  marriage-rate  and  the  birth-rate  to  fall 
for  a  number  of  years  after  a  period  of  depression.  Since 


BIRTH-  AND   DEATH-RATES  IN   MASSACHUSETTS      213 


3 


^i 
3  .3 


•i 


214          DEATH-,   BIRTH-  AND  MARRIAGE-RATES 


1892  the  death-rate  has  decreased  considerably.  The 
general  synchronism  between  the  birth-rate  and  the  death- 
rate  should  be  noticed,  —  and  also  the  numerous  excep- 
tions to  the  rule. 

In  recent  years  there  has  been  a  marked  tendency  towards 
uniformity  in  the  death-rate,  not  only  in  the  state  as  a 
whole  from  year  to  year,  but  among  the  subdivisions  of 
the  state  in  any  given  year. 

The  fluctuations  from  year  to  year  are  due  in  part  to 
incorrect  estimates  of  population. 

Monthly  death-rates  in  Massachusetts.  —  The  general 
death-rate  is  not  constant  throughout  the  year,  but  varies 
seasonally.  There  are  several  ways  in  which  this  may  be 
shown.  The  following  figures  are  for  the  state  of  Massa- 
chusetts for  the  year  1915. 

TABLE  51 
MONTHLY  DEATH-RATES:  MASSACHUSETTS,   1915 


Month. 

Rate. 

Per  cent  of 
annual  rate. 

(1) 

(2) 

(3) 

Jan. 
Feb. 
Mar. 

14.65 
13.60 
16.80 

102 
C4 
117 

Apr. 
May 
June 

17.45 
13.95 
12.35 

121 
97 

86 

July 
Aug. 

Sept. 

12.55 
13.10 
13.75 

87 
91 
96 

Oct. 
Nov. 
Dec. 

13.40 
13.10 
16.00 

93 
91 
111 

Year 

14.40 

100 

MARRIAGE-RATES  IN  MASSACHUSETTS  215 

Monthly  rates  vary  considerably  from  year  to  year  in 
the  same  place  and  are  different  for  different  places. 
Climatic  conditions  have  an  influence  on  these  short  term 
rates.  The  chance  occurrence  of  communicable  diseases 
also  has  its  effect.  Weekly  rates  fluctuate  even  more 
widely  than  monthly  rates,  and  daily  rates  a  fortiori. 

The  ten  year  average  for  Massachusetts  for  1905-14  gave 
the  highest  winter  rate  for  February  and  not  for  April  as 
in  1915;  and  the  highest  summer  rate  was  in  August,  not 
September  as  in  1915. 

The  student  should  compute  and  study  monthly  rates 
for  places  where  the  climatic  conditions  are  different. 

Marriage-rates  in  Massachusetts.  —  Marriage-rates  rise 
and  fall  periodically.  The  rate  is  influenced  by  social  and 
economic  conditions,  by  the  age  distribution  of  the  popu- 
lation, the  ratio  of  the  sexes  at  marriageable  age,  by  nation- 
ality, and  by  many  causes.  There  has  been  no  steady 
downward  trend  in  the  marriage-rate  as  in  the  case  of  the 
death-rate  and  birth-rate.  There  is,  however,  a  seasonal 
variation.  June  and  October  are  the  most  popular  months 
for  weddings. 

In  1915  the  Massachusetts  marriage-rate  for  the  year  was 
17.0;  in  June  it  was  27.5,  in  October,  23.9,  but  in  March 
only  6.6.  There  were  four  times  as  many  weddings  in  June 
as  in  March. 

Since  1870  the  median  marriage-rate  in  Massachusetts 
has  been  18.0.  After  the  panic  of  1873  the  annual  rates  for 
several  years  ranged  between  15  and  16.5,  and  after  other 
periods  of  business  depression  they  have  been  below  17. 
The  highest  annual  rate  in  nearly  fifty  years  was  during 
1871  and  1872,  when  it  was  21.1  per  thousand. 

The  published  statistics  of  marriages  generally  include 
tables  classified  according  to  the  age  and  nativity  of  the 
bride  and  groom ;  the  number  of  the  marriage  (whether  first, 


216          DEATH-,   BIRTH-  AND  MARRIAGE-RATES 

second,  third,  etc.);  and  the  previous  state  of  the  persons 
wed  (whether  bachelors,  maids,  widowers,  or  widows). 

Divorce-rate  in  Massachusetts.  —  In  1915  the  number 
of  persons  divorced  was  1.22  per  1000  population;  in  1914 
the  rate  was  1.21;  in  1910,  1.15;  in  1890,  0.58;  in  1870, 
0.52. 

Limited  use  of  general  death-rates  (gross  rates).  - 
General  death-rates  are  composite  figures.  They  cover 
the  entire  population,  both  sexes,  all  ages  and  nationali- 
ties, all  occupations,  all  causes  of  death,  while  the  estimates 
of  population  are  often  inaccurate.  Fluctuations  from  year 
to  year  depend  in  part  on  the  size  of  the  population,  in  part 
upon  the  composition  of  the  population,  as  well  as  upon 
causes  of  death.  Under  these  conditions  it  is  evident  that 
they  cannot  be  safely  used  as  an  index  of  mortality  condi- 
tions in  different  places  and  for  long  periods  of  time  in  any 
one  place. 

A  general  death-rate,  or  gross  death-rate,  is  of  little  use 
until  it  has  been  analyzed. 

The  " total  solids"  in  a  water  analysis  gives  the  chemist 
almost  no  idea  of  the  quality  of  the  water :  it  is  necessary  to 
separate  the  "  solids  "  into  their  constituent  parts.  In  the 
same  way  a  general  death-rate  must  be  broken  up  into  its 
constituent  parts.  At  the  present  time  the  analysis  of 
death-rates  is  practiced  but  little.  Death-rate  analysis 
today  is  in  about  the  same  condition  that  water  analysis 
was  in  fifty  years  ago. 

The  necessary  analysis  cannot  be  made  until  the  im- 
portant subject  of  specific  death-rates  has  been  considered 
in  the  next  chapter. 

The  ideal  death-rate.  —  Is  there  such  a  thing  as  an  ideal 
death-rate?  At  present  our  general  death-rates  are  falling. 
They  cannot  continue  to  fall  forever,  for  man  is  mortal 
and  all  must  die?  A  large  part  of  the  decrease  in  the 


THE  IDEAL  DEATH-RATE  217 

death-rate  can  be  traced  to  sanitary,  hygienic  and  medical 
improvements.  Another  part  may  be  due  to  a  lowering 
birth-rate  following  a  relatively  high  birth-rate,  or  in  other 
words  to  an  increasing  ratio  of  persons  in  the  young  and 
middle-aged  groups.  This  condition  will  not  continue 
permanently.  In  due  course  the  young  will  become  middle 
aged  and  the  middle  aged  will  become  old,  the  excess  of 
population  will  enter  those  age-groups  where  the  specific 
death-rates  are  high  and  this  will  cause  the  general  death- 
rate  to  rise.  Or  the  birth-rate  will  rise  and  temporarily 
this  will  raise  the  general  death-rate. 

Unless  public  health  officials  learn  how  to  view  general 
death-rates  in  a  proper  light  —  a  good  way  being  not  to 
view  them  at  all  —  they  may  be  surprised  and  discouraged 
some  day  to  find  that  the  death-rate  is  rising. 

The  Great  War  in  a  most  horrible  and  pitiful  way  cut 
out  a  large  number  of  males  in  the  middle-aged  groups  in 
many  countries.  Temporarily  this  will  increase  the  gen- 
eral death-rate.  On  the  other  hand  these  young  men  will 
not  live  to  enter  the  old-age  groups  where  the  specific 
death-rates  are  high.  What  effect  will  this  have  on  the 
future  trend  of  the  death-rate?  What  effect  will  it  have  on 
the  birth-rate? 

Perhaps  it  may  be  for  the  best  interest  of  the  race  that 
the  general  death-rate  be  higher  than  it  now  is.  This 
would  be  the  case  if  there  should  be  more  babies  and  more 
grandfathers  and  grandmothers.  To  answer  the  ques- 
tion as  to  what  is  the  lowest  practicable  death-rate  we 
must  first  decide  what  is  an  ideal  distribution  of  popula- 
tion as  to  age  and  sex,  and  then  consider  what  diseases  at 
the  different  ages  we  can  reasonably  expect  to  eliminate. 
It  is  an  interesting  problem  for  thought  and  discussion. 


218         DEATH-,   BIRTH-  AND  MARRIAGE-RATES 


EXERCISES  AND    QUESTIONS 

1.  Plot  the  general  death-rates  of  Massachusetts  by  years  from  1850 
to  date.     Connect  the  points  with  straight  lines.     Then  draw  straight 
lines  connecting  the  death-rates  for  the  years  divisible  by  ten.     Why  is 
the  resulting  curve  so  regular?     Connect  the  points  for  years  ending  in 
9.     Why  is  the  resulting  curve  so  irregular? 

2.  Compare  the  published  statistics  for  tuberculosis  as  given  by 
local,  state  and  federal  authorities.     Explain  the  differences.      [See  Am. 
J.  P.  H.,  May  1913,  p.  431.] 

3.  Compute  the  following  death-rates,  carrying  the  results  only  as 
far  as  accuracy  warrants. 


Population 

Deaths  per  year 

5,461,200 

70,210 

261,500 

2,913 

35,000 

421 

5,260 

98 

897 

17 

4.  How  does  the  marriage-rate  ordinarily  compare  with  the  ratio  of 
marriages  to  persons  eligible  to  marriage  (bachelors,  spinsters,  widowers, 
widows  and  divorced  persons,  all  of  marriageable  age)?     [Newsholme's 
"Vital  Statistics,"  p.  58.] 

5.  How  do  the  marriage-rates  hi  cities  compare  with  those  in  rural 
districts? 

6.  Is  the  marriage-rate  a  reliable  "barometer  of  prosperity,"  as  Dr. 
Farr  called  it? 

7.  What  effect  has  war  on  the  marriage-rate? 

8.  What  proportion  of  marriages  are  remarriages? 

9.  Are  remarriages  more  common  among  widowers  or  widows? 

10.  Prepare  a  table  showing  the  marriage  state   (single,  married, 
widowed,  divorced)  of  the  population  of  some  civil  division  for  each 
sex  and  for  different  age-groups  above  age  fifteen.     [Consult  census 
reports.] 

11.  At  what  ages  do  people  in  different  social  positions  marry? 


EXERCISES  AND  QUESTIONS  219 

12.  What  changes,  if  any,  have  taken  place  in  the  age  of  marriage 
among  people  of  different  social  position  during  recent  years? 

13.  How  do  the  general  birth-rates  for  urban  and  rural  districts 
compare  with  each  other? 

14.  How  do  the  birth-rates  for  urban  and  rural  districts  compare 
with  each  other  if  based  on  the  number  of  married  women  of  child- 
bearing  age? 

15.  What  relation  is  there  between  birth-rates  based  on  married 
women  of  child-bearing  age  and  the  social  position  of  these  women? 

16.  What  relation  is  there  between  the  birth-rate  thus  computed 
and  the  age  of  marriage? 

17.  What  influence  has  war  on  the  general  birth-rate? 

18.  What  influence  has  national  prosperity  on  fecundity? 

19.  How  do  the  general  birth-rates  compare  for  different  political 
countries,  such  as  England,  Ireland,  France,  Germany,  Austria,  Bel- 
gium, etc. 

20.  How  do  the  birth-rates  for  different  nationalities  in  the  United 
States  compare  with  each  other? 

21.  How  does  the  birth-rate  for  the  Irish  in  Ireland  compare  with 
that  of  the  Irish  in  Massachusetts? 

22.  How  do  the  birth-rates  among  Catholics  compare  With  that 
among  Protestants?    Consult  the  statistics  of  Canada,  especially  the 
provinces  of  Ontario  and  Quebec. 

23.  What  is  the  ratio  of  males  to  females  among  births? 

24.  What  is  the  ratio  of  males  to  females  among  still-births? 

25.  What  is  the  ratio  of  males  to  females  among  illegitimate  "births? 


CHAPTER  VII 
SPECIFIC   DEATH-RATES 

Although  general  death-rates  have  their  uses,  something 
more  is  needed  if  statistics  of  mortality  are  to  be  used 
to  their  best  advantage.  The  tendencies  of  human  beings 
to  die  are  not  constant;  diseases  differ]  in  their  fatality; 
persons  of  different  age  differ  in  susceptibility  to  disease; 
sex,  nationality,  connubial  condition  are  likewise  variable 
factors.  One  cannot  properly  use  mortality  statistics  in 
public  health  work  without  taking  these  factors  into  ac- 
count, at  least  without  considering  the  most  important  of 
them.  This  brings  us  to  a  consideration  of  specific  death- 
rates.  General  death-rates  are  ratios  between  the  entire 
population  of  a  given  place  and  all  deaths  which  occur  in 
a  year.  We  may  restrict  these  rates  in  several  ways. 

Restrictions  of  death-rates.  —  We  may  consider  a 
shorter  period  than  a  year,  and  compute  the  rate  for  a  month 
or  a  week  and  thus  obtain  a  partial  rate  or  a  short-term 
rate  as  described  in  the  previous  chapter.  This,  however, 
is  not  usually  classed  as  a  specific  rate. 

We  may  restrict  the  computation  to  a  special  class  or 
group  of  the  population ;  that  is,  we  may  take  into  account 
only  males  or  only  females  and  compute  the  death-rate 
for  them  alone.  These  would  be  specific  death-rates  by 
sex.  We  may  consider  each  age-group  by  itself  and  find 
the  death-rate  for  it  alone.  This  would  be  to  compute 
specific  death-rates  by  age-groups.  Or  we  may  take  only 
persons  of  the  same  nationality  or  occupation  and  com- 
pute specific  death-rates  for  them. 

220 


AGE  221 

Again  we  may  consider  separately  the  different  causes  of 
death,  and  compute  specific  death-rates  for  tuberculosis, 
for  scarlet  fever,  or  for  cancer. 

Finally  we  may  consider  particular  diseases  and  at  the 
same  time  restrict  the  computation  to  certain  classes  or 
groups  of  people;  thus  we  may  compute  the  "  typhoid 
fever  death-rate  for  males  in  age  group  15-19  years." 

It  has  been  suggested  that  these  various  modes  of  re- 
striction might  be  designated  by  such  expressions  as 
" special  death-rates,"  " particular"  rates,  "limited"  rates, 
etc.,  but  apparently  the  common  expression  "  specific  " 
death-rate  serves  every  useful  purpose. 

It  is  the  purpose  of  the  present  chapter  to  describe  the 
methods  of  computing  specific  rates  and  to  call  attention 
to  their  importance.  It  is  not  too  much  to  say  that  an 
understanding  of  specific  rates  is  the  key  to  the  interpretation 
of  vital  statistics.  Failure  to  appreciate  the  important  influ- 
ences of  age  is  alone  responsible  for  scores  of  fallacious 
conclusions  derived  from  tables  of  vital  statistics. 

Age.  —  The  span  of  human  life  has  been  divided  into  age 
periods  in  many  different  ways.  Shakespeare1  vividly 
describes  the  seven  ages  of  man. 

Jaques:    All  the  world's  a  stage, 
And  all  the  men  and  women  merely  players: 
They  have  their  exits  and  their  entrances; 
And  each  man  in  his  time  plays  many  parts, 
His  acts  being  seven  ages.     At  first  the  infant, 
Mewling  and  puking  in  the  nurse's  arms; 
Then  the  whining  school-boy,  with  his  satchel 
And  shining  morning  face,  creeping  like  snail 
Unwillingly  to  school;  and  then  the  lover, 
Sighing  like  furnace,  with  a  woeful  ballad 
Made  to  his  mistress'  eyebrow;  then  a  soldier, 
Full  of  strange  oaths  and  bearded  like  the  pard, 

1  Jaques  in  As  You  Like  It,  Act  II,  Scene  VII. 


222  SPECIFIC  DEATH-RATES 

Jealous  in  honour,  sudden  and  quick  in  quarrel, 
Seeking  the  bubble  reputation 
Even  in  the  cannon's  mouth;  and  then  the  justice, 
In  fair  round  belly  with  good  capon  lin'd, 
.  With  eyes  severe  and  beard  of  formal  cut, 
Full  of  wise  saws  and  modern  instances; 
And  so  he  plays  his  part;  the  sixth  age  shifts 
Into  the  lean  and  slipper'd  pantaloon, 
With  spectacles  on  nose  and  pouch  on  side, 
His  youthful  hose  well  sav'd,  a  world  too  wide 
For  his  shrunk  shank;  and  his  big  manly  voice, 
Turning  again  toward  childish  treble,  pipes 
And  whistles  in  his  sound;  last  scene  of  all, 
That  ends  this  strange  eventful  history, 
Is  second  childishness  and  mere  oblivion, 
Sans  teeth,  sans  eyes,  sans  taste,  sans  every  thing. 

Just  where  to  draw  the  age  lines  between  Shakespeare's 
seven  ages  is  a  most  difficult  matter  and  it  would  be  hard 
to  get  any  two  people  to  agree.  The  divisions  suggested  in 
Fig.  47  are  merely  for  provoking  discussion. 

Physiologically  seven  fairly  distinct  states  may  be  recog- 
nized —  the  pre-natal  state,  infancy,  childhood,  youth 
(maidenhood),  early  manhood  and  manhood  (child-bear- 
ing age  and  maturity),  and  finally  old  age,  or  senility. 
The  age  limits  of  the  early  groups  are  fairly  well  marked. 
The  later  groups  are  more  indistinct.  He  would  be  a  bold 
person  who  would  undertake  to  establish  an  age  limit  for 
senility.  Every  one  knows  what  was  said  about  Dr. 
Osier  when  he  attempted  to  do  something  of  that  sort.  In 
Fig.  47  the  biblical  limit  of  "  three  score  years  and  ten  " 
has  been  used.  The  author  believes  that  he  may  safely 
hide  behind  that.  The  division  between  childhood  and 
youth  in  boys  is  perhaps  not  quite  the  same  as  the  division 
between  childhood  and  maidenhood  in  girls. 

From  the  standpoint  of  environment  there  are  several 
fairly  distinct  age  periods.  Infancy  in  this  case  means  the 


AGES  OF  MAN 


223 


20 


40 


Envlroment 


Physiological  State 


Shakespeares 

Seven  Ages 

of  Man 


Occurence  of 

Diseases 

Per  cent  per  year 
( After  Eearson) 


Specific  death  rate, 
according  to  age. 


0        10       20       30       40       50       60       70       80       90      100 
FIG.  47.  —  Ages  of  Man. 


224  SPECIFIC  DEATH-RATES 

earliest  period,  in  which  the  environment  is  maternal.  It 
terminates  when  the  child  is  weaned.  Then  follows  the 
period  of  home  environment.  Later  the  school  environ- 
ment controls.  After  that  the  work  place  comes  in  as  an 
important  factor.  Of  course  the  home  influence  continues 
through  life,  and  in  the  case  of  most  women  it  predominates 
after  the  school  age.  Indeed  after  the  school  age  the 
environment  becomes  complex. 

Karl  Pearson  has  analyzed  the  curve  which  shows  the 
age  distribution  of  deaths  in  an  interesting  way.  He  con- 
cludes that  there  are  five  groups  of  diseases,  those  of  in- 
fancy, childhood,  youth,  middle  age  and  old  age.  All  of 
these  extend  over  wide  limits,  but  culminate  at  the  ages 
shown  in  Fig.  47.  One  may  die  of  an  old  age  disease  at 
thirty,  or  one  may  have  a  children's  disease  at  forty. 
Endless  complications  exist  in  special  cases,  yet  in  the  main 
the  distinctions  between  the  five  classes  of  diseases  are  well 
known. 

At  the  bottom  of  the  diagram  we  see  the  curve  which 
shows  the  specific  death-rate  in  its  characteristic  variations 
through  the  span  of  life.  This  curve  in  its  general  form  is 
the  same  for  both  sexes,  for  all  nationalities,  for  all  climates. 
There  are  differences,  of  course,  but  over  all  the  other 
factors  which  influence  death,  age  predominates.  This 
curve,  it  should  be  observed,  is  based  on  deaths  from  all 
causes.  It  would  not  necessarily  apply  to  particular  diseases. 

The  student  should  study  this  curve  of  specific  death- 
rates  according  to  age  until  he  can  reproduce  it  with  ap- 
proximate accuracy  from  memory. 

Vision  of  Mirza.  —  Those  who  do  not  enjoy  studying 
statistics  may  appreciate  the  following  paragraph  taken 
from  Addison's  "  Vision  of  Mirza/' 

"  The  bridge  thou  seest,  said  he,  is  Human  Life;  con- 
sider it  attentively.  Upon  a  more  leisurely  survey  of  it, 


HOW  TO  COMPUTE  SPECIFIC  DEATH-RATES     225 

I  found  that  it  consisted  of  threescore  and  ten  entire  arches, 
with  several  broken  arches,  which,  added  to  those  that  were 
entire,  made  up  the  number  about  an  hundred.  As  I  was 
counting  the  arches,  the  Genius  told  me  that  this  bridge 
consisted  at  first  of  a  thousand  arches;  but  that  a  great  flood 
swept  away  the  rest,  and  left  the  bridge  in  the  ruinous  con- 
dition I  now  beheld  it.  But  tell  me  further,  said  he, 
what  thou  disco verest  on  it.  I  see  multitudes  of  people 
passing  over  it,  said  I,  and  a  black  cloud  hanging  on  each 
end  of  it.  As  I  looked  more  attentively,  I  saw  several  of 
the  passengers  dropping  through  the  bridge  into  the  great 
tide  that  flowed  underneath  it:  and  upon  further  exami- 
nation perceived  that  there  were  innumerable  trap-doors 
that  lay  concealed  in  the  bridge  which  the  passengers  no 
sooner  trod  upon,  but  they  fell  through  them  into  the  tide, 
and  immediately  disappeared.  These  hidden  pit-falls 
were  set  very  thick  at  the  entrance  of  the  bridge,  so  that 
throngs  of  people  no  sooner  break  through  the  cloud,  but 
many  of  them  fell  into  them.  They  grew  thinner  towards 
the  middle,  but  multiplied  and  laid  closer  together  towards 
the  end  of  the  arches  that  were  entire.  There  were,  in- 
deed, persons,  but  their  number  was  very  small,  that  con- 
tinued a  kind  of  hobbling  march  of  the  broken  arches,  but 
fell  through  one  after  another,  being  quite  tired  and  spent 
with  so  long  a  walk." 

How  to  compute  specific  death-rates.  —  The  specific 
death-rate  for  any  age-group  is  found  by  dividing  the 
number  of  deaths  of  persons  whose  ages  lie  within  the 
group  limits  by  the  number  of  thousands  of  persons  in 
the  same  group  alive  at  mid-year.  The  computation  is  pre- 
cisely the  same  as  that  for  the  general  death-rate  except 
that  both  deaths  and  population  are  confined  to  specific 
age-groups.  If  both  quantities  are  known  the  process  is 
merely  arithmetical. 


226 


SPECIFIC  DEATH-RATES 


Example:  —  Given  the  following  data  for  New  South 
Wales,  1901  (Columns  1,  2,  3). 

TABLE  52 


Age-group. 

Population. 

Deaths. 

Specific  deatl-- 
rate. 

(1) 

(2) 

(3) 

(4) 

0-1 

40,500 

3,234 

79.9 

1-19 

704,000 

1,960 

2.8 

20-39 

514,900 

2,251 

4.4 

40-59 

256,600 

2,965 

11.6 

60- 

89,800 

5,400 

60.1 

Total 

1,605,800 

15,810 

9.85 

To  find  the  specific  death-rate  for  the  age-group  1-19 
years,  divide  the  number  of  deaths  in  that  group,  i.e.,  1960 
by  704,  the  number  of  thousands  of  population.  The  result 
is  2.8  per  1000.  Similarly  the  specific  death-rate  for  age- 
group  20-39  is  2251  +  515  =  4.4  per  1000.  The  figures 
in  Column  4  were  thus  computed.  The  total  deaths  di- 
vided by  the  total  population,  in  thousands,  gives  the  gen- 
eral death-rate,  i.e.,  15810  -f-  1605.8  =  9.85  per  1000. 

If  the  number  of  deaths  within  the  age-group  is  known 
but  the  population  is  unknown,  it  is  necessary  to  estimate 
the  population  in  the  group.  This  can  usually  be  done  with 
sufficient  accuracy  from  the  data  provided  by  the  censuses. 
The  methods  of  making  these  estimates  both  for  censal  and 
non-censal  years  has  been  already  described.  This  may 
involve  a  redistribution  of  the  population  from  those  given 
in  the  census  to  those  corresponding  to  the  death  statistics. 

If  the  population  in  the  group  is  known  but  the  number 
of  deaths  is  unknown  the  computation  cannot  be  made  with 
accuracy.  It  might  be  possible  to  redistribute  the  deaths 
into  age-groups  corresponding  to  the  population,  but 


DEATH-RATES  BY  AGES  FOR  MALES  AND  FEMALES     227 


SPECIFIC   DEATH  RATES 

OF 
MALES  AND  FEMALES 

IN 
ORIGINAL  REGISTRATION  STATES 

1910 

FROM  U.S.  LIFE  TABLES  PREPARED 
BY  PROF.  JAMES.  W.  GLOVER,  FOR 
THE  BUREAU  OF  THE  CENSUS,  1916 


40  50  60 

Age  in  Years 

FIG.  48.  —  Specific  Death-rates. 

specific  death-rates  obtained  in  this  way  would  in  most 
cases  be  unreliable. 

Specific  death-rates  by  ages  for  males  and  females.  - 
Looking  at  the  two  curves  for  the  specific  death-rates  of 
males  and  females  shown  in  Fig.  48  one  would  say  at  first 
that  they  were  much  alike,  but  that  the  rates  at  all  ages  were 


228 


SPECIFIC   DEATH-RATES 


higher  for  males  than  for  females.  In  a  general  way  this  is 
true,  but  a  closer  study  shows  that  the  differences  are  not 
the  same  for  all  ages.  The  table  from  which  these  curves 
were  plotted  gave  data  from  which  the  following  figures 
were  obtained. 

TABLE  53 

PER  CENT  BY  WHICH  THE  SPECIFIC  DEATH-RATES  FOR 
MALES  EXCEEDED  THOSE  FOR  FEMALES  IN  VARIOUS 
AGE  INTERVALS 

(Based  on  the  original  registration  states;  population  in  1910,. and 
deaths  in  1909,  1910  and  1911). 


Age  interval. 

Per  cent 
(approximate). 

Age  interval. 

Per  cent 
(approximate). 

(1) 

(2) 

(3) 

(4) 

yr. 

yr. 

0-1 

20 

55-56 

14 

5-6 

5 

60-61 

19 

10-11 

15 

65-66 

14 

'15-16 

5 

70-71 

10 

20-21 

15 

75-76 

12 

25-26 

6      . 

80-81 

8 

30-31 

10 

85-86 

7 

35^-36 

20 

90-91 

3 

40-41 

35 

95-100 

2 

45-46 

27 

100-101 

3 

50-51 

23 

In  infancy  the  death-rate  for  males  exceeds  that  for 
females  by  20  per  cent.  Between  five  and  twenty-five  years 
of  age  the  differences  vary  considerably  in  successive  years 
but  average  about  10  per  cent.1  Above  age  twenty-five 
the  male  death-rate  begins  to  exceed  the  female  death-rate 
-by  considerable  amounts  and  this  continues  to  the  age  of 
forty,  when  the  excess  is  35  per  cent.  After  that  it  steadily 
decreases.  In  old  age  the  two  rates  are  much  alike.  It 
must  be  remembered  that  these  figures  are  for  a  certain 

1  The  error  of  population  due  to  concentration  on  round  numbers 
probably  accounts  for  some  of  these  differences. 


EFFECT  OF  MARITAL  CONDITION  ON  DEATH-RATES    229 


limited  area  and  for  a  short  interval  of  time  and  for  a  par- 
ticular composition  of  people  with  respect  to  nationality, 
birth-rate,  and  so  on.  They  are  to  be  regarded  merely  as 
illustrative  of  the  differences  between  males  and  females. 
What  are  the  reasons  for  the  differences  here  shown? 

Effect  of  marital  condition  on  specific  death-rates.  — 
Students  will  find  it  interesting  to  compute  specific  death- 
rates  for  males  and  females  according  to  their  marital  con- 
dition. It  will  be  found  that  the  rates  for  single  men  are 
considerably  higher  than  for  married  men.  Between  thirty 
and  forty  years  of  age  they  may  be  nearly  twice  as  high;  at 
higher  ages  the  percentage  differences  become  less.  The 
death-rates  of  single  females  are  higher  than  those  of 
married  females  except  that  during  part  of  the  child-bearing 
period,  —  say  from  twenty  to  forty-five,  —  the  rates  are 
higher  for  married  wornen. 

Professor  Walter  F.  Willcox,  of  Cornell  University,  has 
computed  the  following  specific  death-rates  for  New  York 
State,  the  cities  of  New  York  and  Buffalo  excluded,  for 
1909-1911,  arranged  by  age-groups  and  by  classes  corre- 
sponding to  marital  condition,  as  follows: 

TABLE-  54 

SPECIFIC  DEATH-RATES  ACCORDING  TO  AGE  AND 
MARITAL  CONDITIONS,   NEW  YORK,   1909-11 


Males. 

Females. 

Age-group. 

Single. 

Married. 

Widowed  or 
divorced. 

Single. 

Married. 

Widowed  or 
divorced. 

(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

(7) 

20-29 

6.6 

4.2 

12.0 

4.7 

5.7 

9.4 

30-39 

12.9 

5.9 

14.1 

7.4 

6.3 

9.5 

40-49 

19.5 

9.5 

17.3 

10.0 

8.2 

12.1 

50-59 

28.7 

17.0 

30.5 

19.9 

14.5 

18.8 

60-69 

51.0 

31.9 

48.6 

37..  1 

28.1 

38.2 

70-79 

101.4 

72.7 

96.0 

82.2 

61.4 

87.2 

80- 

204.2 

205.1 

315.7 

279.8 

194.8 

269.8 

230  SPECIFIC  DEATH-RATES 

Among  the  theories  suggested  in  explanation  of  these 
differences  is  the  effect  of  leading  a  better  supervised  and 
more  restrained  life  among  married  persons,  the  better 
economic  conditions  of  the  married,  the  effect  of  marriage 
selection  and  the  effect  of  the  marriage  relation  itself. 

Nationality  and  specific  death-rates.  —  Specific  death- 
rates  for  different  ages  and  sexes  are  not  the  same  for  all 
nationalities.  It  is  very  difficult,  however,  to  say  how  much 
of  this  is  due  to  racial  difference  and  how  much  is  due  to 
environmental  conditions;  that  is,  it  is  hard  to  separate 
the  physiological  from  the  social  and  economic  factors. 
Practically,  however,  these  factors  must  be  considered 
together  in  discussing  nationalities  in  the  United  States. 
We  see  these  differences  well  marked  between  the  negro  and 
the  white  populations  of  the  original  registration  states. 
The  figures  in  Table  55,  taken  from  Professor  Glover's  re- 
port, will  show  this. 

The  figures  in  this  table  are  carried  to  an  unnecessary 
degree  of  precision  so  far  as  this  particular  point  is  concerned 
and  in  the  case  of  the  advanced  ages  for  negroes  probably 
not  even  the  whole  numbers  are  accurate.  The  rate  for 
male  negroes  is  almost  double  that  for  male  whites  up  to 
the  age  of  sixty  or  thereabouts;  above  eighty  the  rate  for 
negroes  is  lower  than  for  whites.  Substantially  the  same 
relations  hold  for  white  and  colored  females. 

It  should  be  noticed  that  in  these  various  comparisons 
the  effect  of  age  is  a  factor  which  must  never  be  left  out  of 
account. 


EFFECT  OF  AGE   COMPOSITION  ON  DEATH-RATE      231 


TABLE  55 

SPECIFIC  DEATH-RATES   FOR  WHITE   AND   NEGRO    MALES 
United  States,  Original  Registration  States,  1910 


Rates  per  1000. 

A       '    t          1 

White. 

Negro. 

(1) 

(2) 

(3) 

0-1 

123.26. 

219.35 

5^6 

4.71 

8.56 

10-11 

2.38 

5.02 

15-16 

2.83 

7.87 

20-21 

4.89 

11.96 

25^-26 

5.54 

12.28 

30-31 

6.60 

14.96 

35-36 

8.52 

17.28 

4(M1 

10.22 

21.03 

45-46 

12.64 

23.99 

50-51 

15.53 

31.42 

55-56 

21.50 

39.50 

60-61 

30.75 

50.79 

65-66 

43.79 

64.33 

70-71 

62.14 

83.98 

75^-76 

92.53 

112.77 

80-81 

135.75 

131.27 

85-86 

191.11 

179.82 

90-91 

255.17 

201.01 

95-96 

324.86 

227.76 

100-101 

427.46 

336.29 

Effect  of  the  age  composition  of  a  population  on  the 
death-rate.  —  It  is  evident  also,  from  our  acquired  knowl- 
edge of  specific  death-rates,  that  the  general  death-rates  of 
two  places  cannot  be  reasonably  compared  unless  the  age 
composition  of  the  population  is  substantially  the  same  in 
the  two  places.  The  following  simple  example  will  make 
this  plain: 

Two  places,  A  and  B,  have  the  same  total  population, 
i.e.,  50,000;  and  they  have  the  same  specific  death-rates  at 


232 


SPECIFIC  DEATH-RATES 


different  ages.  The  ages  of  the  people,  however,  differ  as 
shown  in  the  table.  From  these  figures  we  may  compute 
the  general  death-rate  for  each  place. 

TABLE  56 

EFFECT  OF  AGE  COMPOSITION  OF  POPULATION  ON 
THE  GENERAL  DEATH-RATE 


Age. 

Population. 

Specific 
death-rate 
per  1000. 

Computed  deaths. 

Computed 
death-rates 
per  1000. 

A 

B 

A 

B 

A 

B 

(I) 

(2) 

(3) 

(4) 

(5) 

(6) 

(7) 

(8) 

0-4 
5-59 
60-79 

Total 

10,000 
35,000 
5,000 

20,000 
20,000 
10,000 

25 
10 

60 

250 
350 
300 

500 
200 
600 

50,000 

50,000 

900 

1300 

18 

26 

In  B,  a  place  with  a  large  number  of  children  and  eld 
people,  the  rate  is  26  per  1000,  while  in  A,  a  place^with  a 
large  middle-aged  population,  the  rate  is  only  18.  This 
is,  of  course,  an  exaggerated  case,  but  slight  differences  in 
age  distribution  make  a  greater  difference  in  the  general 
death-rate  than  one  would  suppose. 

In  1899,  according  to  a  report  of  the  U.  S.  Secretary  of 
War,  the  annual  death-rate  of  soldiers  in  the  Philippines 
was  17.20,  while  the  death-rate  of  Boston  was  20.09,  of 
Washington  20.74  and  of  San  Francisco  19.41.  The  ob- 
vious inference  was  that  the  mortality  in  the^army  com- 
pared favorably  with  the  mortalities  of  the  cities  mentioned. 
The  facts  unstated  were  that  soldiers  are  picked  men  in  a 
limited  age-group  while  the  cities  contain  a  conglomerate 
population.  A  better  comparison  would  have  §een  one 
between  the  soldiers  and  males  between  20  and  40  years  of 
age  in  the  United  States,  the  usual  death-rate  for  which  is 


EFFECT  OF  AGE  COMPOSITION  ON   DEATH-RATE      233 


less  than  10  per  1000.  Hence  the  mortality  among  the 
troops  in  the  Philippines  was  nearly  twice  as  high  as  that 
of  males  of  similar  age  in  the  United  States. 

In  1911  the  general  death-rate  of  Chicago  was  14.5  and 
that  of  Cambridge,  Mass.,  was  15.2.  Was  Chicago  the 
healthier  city?  No,  indeed!  The  following  figures  show 
that  the  specific  death-rates  were  lower  in  Cambridge  for 
all  ages  except  the  age-intervals  of  10-19  years  and  65  years 
and  over.  The  reason  for  Chicago's  lower  rate  was  because 
there  were  relatively  more  people  in  Chicago  at  those 
middle  ages  where  the  specific  death-rates  are  naturally 
low. 

TABLE  57 

COMPARISON   OF  DEATH-RATES  IN  CAMBRIDGE,  MASS., 
AND  CHICAGO 


Per  cent  of  population  in 
age-groups.    Both  sexes. 

Specific  death-rates  per  1000, 
in  1911. 

Age  in  years. 

1910.     • 

Cambridge. 

Chicago. 

Cambridge. 

Chicago. 

(1) 

(2) 

(3) 

(4) 

(5) 

Under  5 

10.3 

10.2 

39.1 

39.5 

5-9 

9.1 

8.8 

4.3 

4.7 

10-14 

8.5 

8.6 

3.5 

2.6 

15-19 

8.5 

9.6 

4.6 

3.7 

20-24 

9.9 

11.5 

3.8 

5.3 

25-34 

18.2 

19.7 

5.5 

6.9 

35-44 

15.0 

14.5 

9.0 

11.4 

45-54 

16.0 

9.6 

16.0 

19.3 

55-64 

4.5 

29.4 

35.1 

65-74 

4.5 

2.0 

64.0 

63.6 

75  and  over  (in- 

cluding unknown) 

1.0 

148.8 

144.2 

Total 

100.0 

100.0 

15.2 

14.5 

Obviously  the  two  general  death-rates  tell  us  very  little 
that  we  want  to  know  —  that  is,  not  until  they  have  been 
analyzed. 


.234  SPECIFIC   DEATH-RATES 

Effect  of  race  composition  on  death-rates.  —  If  differ- 
ent races  have  different  specific  death-rates  then  the 
general  death-rates  of  two  places  which  have  different 
percentages  of  various  races  cannot  be  fairly  compared.  The 
general  death-rates  of  southern  cities  cannot  be  fairly  com- 
pared with  those  of  northern  cities.  In  1911  the  general 
death-rate  in  New  York  City  was  15.2;  in  Washington  it 
was  18.7;  in  New  Orleans,  20.4.  The  death-rate  for  the 
white  population  in  Washington,  however,  was  only  15.5 
and  in  New  Orleans  only  16.6.  Even  these  figures  are 
not  strictly  comparable  as  they  do  not  take  into  account 
age  distribution. 

Changes  in  specific  death-rates  through  long  periods.  - 
We  have  seen  that  the  general,  or  gross,  death-rates  have 
been  falling  for  a  Itfng  time.  Are  the  same  changes  occur- 
ring in  the  specific  death-rates  at  different  ages  and  for  dif- 
ferent classes  of  the  population?  This  is  a  most  important 
question.  If  we  can  answer  it  we  shall  have  come  close  to 
measuring  the  effect  of  our  sanitary,  hygienic  and  med- 
ical improvements  during  recent  years.  Far  too  little 
effort  has  been  made  to  compile  statistics  of  this  sort.  Let 
us  see  what  we  can  learn  from  Massachusetts  records. 

In  1830  Lemuel  Shattuck  computed  specific  death-rates 
for  Boston.  It  will  be  interesting  to  compare  these  with 
figures  for  the  year  1911,  published  in  the  U.  S.  Mortality 
Statistics  by  the  Bureau  of  the  Census  and  recast  to  make 
the  age-groups  correspond. 


CHANGES  IN  SPECIFIC  DEATH-RATES 


235 


TABLE  58 
SPECIFIC  DEATH-RATES,  BOTH  SEXES,  FOR  BOSTON 


Age  inter- 

Rate per  1000. 

val. 

1830. 

1911. 

(1) 

(2) 

(3) 

(approximate) 

0-1 

161 

1-5 

17 

0-5 

"59'e" 

. 

5-9 

8.1 

•'4" 

10-14 

5.5 

2.4 

15-19 

4.9 

4 

20-29 

10.4 

6 

30-39 

20.1 

10 

40-49 

22.4 

15 

50-59 

29.3 

27. 

60-69 

45.8 

52 

70-79 

92.4 

102 

80-89 

162.1 

90- 

321.4 

During  the  81  years  there  has  been  a  marked  reduction 
in  the  specific  death-rates  at  all  ages  below  sixty.  In  the 
case  of  children  and  youths  the  reduction  was  as  much  as  one 
half.  In  1898  Dr.  Samuel  W.  Abbott,  then  Secretary  of 
the  Massachusetts  State  Board  of  Health,  computed  a  life 
table  for  the  State l  for  the  years  1893-7  in  which  the  spe- 
cific death-rates  were  given  for  certain  age-groups.  It  is 
interesting  to  compare  these  with  the  figures  given  for 
Massachusetts  in  the  U.  S.  Life  Tables  for  1910. 


Ann.  Kept.  1898,  p.  810. 


236 


SPECIFIC  DEATH-RATES 


TABLE  59 
SPECIFIC  DEATH-RATES  FOR  MASSACHUSETTS 


Rate  per  1000 

Rate  per  1000 

1893-7 

1910 

Age-group. 

Age-group. 

Males. 

Females. 

Males. 

Females. 

(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

0-4 

60.12 

52.22 

5-9 

5.69 

5.82 

7-8 

3.37 

3.13 

10-14 

3.11 

3.40 

12-13 

2.27 

2.05 

15-19 

5.29 

5.68 

17-18 

3.43 

3.17 

20-24 

7.48 

7.32 

22-23 

5.16 

4.30 

25-34 

9.33 

8.78 

30-31 

6.60 

5.97 

35-44 

11.19 

10.74 

40-41 

10.00 

8.14 

45-54 

16.67 

14.88 

50-51 

16.05 

12.58 

55-64 

30.42 

26.00 

60-61 

33.15 

27.03 

65-74 

59.67 

51.37 

70-71 

67.91 

56.47 

75-84 

116.20 

99.88 

80-81 

137.43 

123.49 

85-94 

223.50 

184.81 

90-91 

251.53 

244.90 

95- 

429.20 

367.07 

100-101 

483.90 

392.91 

Here  we  see  the  specific  death-rates  still  falling  up  to 
age  sixty.  For  the  later  ages  there  has  been  a  slight  tend- 
ency to  increase.  It  should  be  noticed,  however,  that  the 
age-groups  are  not  quite  the  same  for  the  two  periods. 

In  1830  and  also  in  1893—7  the  specific  rates  at  ages  five  to 
twenty,  or  thereabouts,  were  higher  for  females  than  for 
males,  but  in  1910  the  opposite  was  true. 

If  we  should  make  similar  comparisons  of  specific  death- 
rates  for  other  places  and  for  different  periods  we  should 
almost  always  find  that  in  recent  years  the  rates  have  been 
falling  for  all  ages  below  fifty  or  sixty. 

What  have  been  the  reasons  for  this  reduction?  Un- 
doubtedly improved  sanitary  and  hygienic  conditions, 
advances  in  medical  and  surgical  science  and  the  arts  of 
preventive  medicine  have  tended  to  reduce  the  number  of 


CHANGES  IN  SPECIFIC   DEATH-RATES  237 


20 


200 


ISO 


100 


140 


120 


KM) 


V 


1870    1880    1890    1900    1910    1870    1880    1890    1900   1910 

FIG.  49.  —  Specific  Death-rates  by  Age-Groups,  Massachusetts, 
1870-1910. 


238  SPECIFIC  DEATH-RATES 

cases  of  sickness  and  to  increase  the  percentage  of  recoveries 
of  those  who  are  taken  sick.  This  has  been  especially 
true  in  the  earlier  ages.  But  it  must  not  be  forgotten  that 
changes  in  the  relative  numbers  of  married  and  single 
persons  in  each  sex,  and  of  persons  of  different  national- 
ity, have  also  their  influence.  A  reason  for  the  increase  in 
the  specific  death-rates  above  fifty  or  sixty  years  of  age  has 
been  frequently  discussed  of  late,  namely  an  increase  in  cer- 
tain degenerative  and  organic  diseases.  This  is  important, 
if  true,  but  it  is  a  difficult  thing  to  prove. 

The  fallacy  of  concealed  classification.  —  Now  that  we 
have  come  to  appreciate  the  effect  of  age,  sex,  nationality, 
and  such  factors  on  death-rates,  but  especially  the  factor 
of  age,  we  can  better  understand  what  may  be  called  the 
fallacy  of  concealed  classification.  If  we  classify  males 
according  to  occupation  we  might  find  that  the  death- 
rate  of  bank  presidents  was  higher  than  that  of  newsboys; 
but  this  would  not  be  because  of  different  occupation  but 
because  of  different  ages.  In  classifying  by  occupation  we 
have  concealed  a  grouping  by  age.  If,  in  classifying  the 
employees  of  the  city  of  Boston  or  New  York  by  occupation 
we  distinguish  between  policemen  and  street  cleaners,  we 
might  find  that  we  had  concealed  a  classification  by  nation- 
ality, the  street  cleaners  being  Italians  and  the  policemen 
Irishmen.  Similarly  in  classifying  railroad  employees  into 
conductors  and  brakemen,  we  might  conceal  age  differences, 
and  under  the  class  of  Pullman  porters  we  might  conceal  a 
nationality  difference.  When  we  consider  stenographers  as 
a  separate  class  we  conceal  a  classification  by  sex.  These 
concealed  classifications  and  groupings  are  sometimes  very 
illusive;  they  creep  into  our  statistics  unawares  and  upset 
what  might  otherwise  be  sound  reasoning.  Illustrations 
may  be  found  on  every  hand.  Every  one  who  uses  statis- 
tics should  be  continually  on  the  watch  for  them. 


USE  OF  SPECIFIC  DEATH-RATES  239 

Use  of  specific  death-rates.  —  It  must  be  evident  from 
what  has  been  said  that  in  order  to  compare  the  mortality 
conditions  in  various  places  the  best  way  is  to  compare 
age  with  age,  sex  with  sex,  nationality  with  nationality,  or 
in  other  words  to  compare  the  various  places,  classes  and 
groups  on  the  basis  of  their  specific  death-rates.  To  do  this 
in  great  detail  involves  labor  and  the  use  of  many  figures. 
Hence  there  has  always  been  a  fascination  in  combining  these 
figures  so  as  to  obtain  a  single  figure  which  may  be  regarded 
as  an  index  of  mortality.  There  are  at  least  two  ways  of  do- 
ing this.  If  there  were  such  a  thing  as  a  standard  population 
—  and  several  such  standards  have  been  suggested,  notably 
the  Standard  Million  (see  page  181)  —  and  if  we  knew  the 
specific  death-rates  by  ages  and  sex  for  any  place,  we  could 
apply  these  rates  to  the  standard  population  and  find 
what  the  general  death-rate  would  have  been  in  the  given 
place  if  the  population  had  been  standard.  And  we  might 
do  the  same  for  another  place  and  thus  obtain  figures  for 
the  death-rates  which  could  be  compared  with  some  degree 
of  justice. 

When  general  death-rates  are  adjusted  to  a  standard 
population  in  this  way  the  results  are  called  "  Standardized 
death-rates."  Sometimes  they  have  been  referred  to  as 
"  corrected  "  death-rates,  but  this  is  a  poor  use  of  the  word, 
for  the  process  is  not  one  of  correcting  errors  or  mistakes  and 
the  final  result  is  not  "  correct,"  for  it  does  not  take  into 
account  all  differences  in  population.  Nor  is  the  expression 
"  standardized  "  a  good  one,  because  it  is  not  the  death- 
rate  which  is  standardized,  but  only  the  population.  A 
better  term  is.  "  Death-rates  adjusted  to  a  Standard  Pop- 
ulation." 

In  the  annual  report  of  the  Massachusetts  State  Board 
of  Health  for  1902  may  be  found  another  method  of  "  cor- 
recting "  death-rates,  used  by  Dr.  Samuel  W.  Abbott.  He 


240  SPECIFIC  DEATH-RATES 

took  as  a  standard  the  specific  death-rates  of  Massachusetts 
by  age  and  sex.  He  then  applied  these  to  the  age  and  sex 
groups  of  the  cities  of  the  state,  to  obtain  what  he  called  the 
standard  death-rate  for  each  place.  Then  he  found  the 
ratio  between  the  "  standard  death-rate  "  for  each  place  and 
the  general  death-rate  of  the  state,  and  called  this  the  "  fac- 
tor of  correction."  Finally  he  multiplied  the  actual  general 
death-rate  of  each  place  by  this  factor  to  obtain  his  "  cor- 
rected death-rate."  The  advantage  of  this  method  was 
that  he  did  not  need  to  use  the  age  distribution  of  deaths 
for  each  place.  The  method  is  interesting,  but  is  not  one 
for  general  adoption,  because  it  would  be  hard  to  decide  on 
a  standard  of  specific  death-rates. 

Another  way  of  using  specific  death-rates  is  that  of  con- 
structing what  are  called  life  tables.  These  will  be  de- 
scribed in  Chapter  XIV. 

But  the  best  way  of  using  specific  death-rates  is  to  use 
them  directly.  To  be  sure  it  means  that  one  must  carry 
more  figures  in  one's  mind.  Instead  of  having  to  think  of 
one  figure  for  the  general  death-rate  it  is  necessary  to  think 
of  figures  for  infant  deaths,  for  the  deaths  of  children,  of 
adults  and  of  the  aged  —  but,  after  all,  are  not  these  the 
really  important  figures?  Statistics  are  worthless  unless 
they  can  be  used.  If  specific  death-rates  are  more  usable 
than  general  death-rates,  we  should  make  the  specific  rates 
more  prominent  and  educate  people  to  think  in  terms  of 
them. 

Death-rates  adjusted  to  a  standard  population.  —  A 
few  examples  will  now  be  given  to  show  how  general  rates 
may  be  adjusted  to  a  standard  population.  .  For  the  sake 
of  simplicity  age  differences  only  will  be  considered.  The 
data  required  are  (a)  the  number  of  deaths  by  age-groups 
in  the  given  place;  (6)  the  number  of  persons  living  at 
mid-year  in  the  corresponding  age-groups;  (c)  an  assumed 


ADJUSTED  DEATH-RATES 


241 


standard  population  for  the  same  age- grouping.  First 
of  all,  therefore,  some  system  of  age-grouping  must  be 
decided  upon.  Let  us  take  first  a  simple  case,  that  is,  one 
.where  there  are  only  a  few  groups. 

On  page  226  were  given  data  for  New  South  Wales,  from 
which  the  specific  death-rates  were  computed.  Let  us 
apply  these  specific  death-rates  to  the  population  of  Sweden 
in  1890  which  we  will  take  as  a  standard.  This  is  given  in 
column  (5)  of  Table  60.  For  age-group  1-19  years  the  spe- 
cific rate  was  2.78  per  1000;  hence,  among  398  persons  the 
number  of  deaths  would  be  0.398  X  2.78  or  1.11  as  given 
in  column  (6).  And  so  for  the  other  age-groups.  The 
figures  in  column  (6) ,  therefore,  give  the  number  of  deaths  in 
each  group  of  the  standard  thousand  of  population,  and 
their  sum  is  the  total  number  of  deaths  in  the  standard 
thousand.  Hence  the  death-rate  of  New  South  Wales  ad- 
justed to  the  standard  population  was  13.44.  This  is 
much  higher  than  the  general  death-rate,  which  was  only 
9.85. 

TABLE  60 
ADJUSTED  DEATH-RATE  FOR  NEW    SOUTH  WALES,   1901 


-Age-^roup  in 
years. 

Population. 

Number  of 
deaths  in 
one  year. 

Specific 
death-rate 
per  1000. 

Standard  age 
distribution 
per  1000. 

Computed 
deaths  per 
1000  of  total 
population. 

(1) 

(2) 

(3) 

(4) 

T5) 

(6) 

0-1 
1-19 
20-39 
40-59 
60  and  over 
Total 

40,500 
704,000 
514,900 
256,600 
89,800 

3,234 
1,960 
2,251 
2,965 
5,400 

79.88 
2.78 
4.37 
11.56 
60.13 

25.5 
398.0 
269.6 
192.3 
114.6 

2.04 
1.11 

1.18 
2.22 
6.89 
13.44 

1,605,800 

15,810 

9.85 

1000.0 

Why  this  difference?  The  answer  is  found  by  comparing 
the  age  distribution  of  the  people  of  New  South  Wales  with 
the  assumed  standard  population. 


242 


SPECIFIC   DEATH-RATES 


TABLE  61 

COMPARISON  OF  POPULATION  DISTRIBUTION  OF  NEW 
SOUTH  WALES  WITH  THAT  OF  SWEDEN  IN    1890 


Age-group. 

New  South  Wales. 

Sweden.           ' 

Number. 

Per  thousand. 

Per  thousand. 

(1) 

(2) 

(3) 

(4) 

0-1 
1-19 
30-39 
40-59 
60- 
All  Ages 

40,500 
704,000 
514,900 
256,600 
89,800 

24.9 
439.0 
320.0 
160.5 
55.6 

25.5 
398.0 
269.6 
192.3 
114.6 

1,605,800 

1000.0 

1000.0 

It  will  be  seen  that  in  New  South  Wales  there  were  fewer 
old  persons,  for  whom  the  specific  death-rates  are  naturally 
high,  but  more  persons  in  middle  life,  for  whom  the  specific 
death-rates  are  naturally  low.  This  is  an  extreme  case,  but 
characteristic  of  a  new  population  built  up  by  immigration. 

Let  us  now  take  a  more  complicated  situation. 

In  1914  there  were  1452  deaths  in  Cambridge,1  Mass., 
distributed  by  age  as  follows: 

TABLE  62 
DISTRIBUTION  OF  DEATHS:    CAMBRIDGE,  MASS.,   1914 


Age. 

Num- 
ber. 

Age. 

Num- 
ber. 

Age. 

Num- 
ber. 

Age. 

Num- 
ber. 

(1) 

(2) 

(1) 

(2) 

(1) 

(2) 

(I) 

(2) 

[o-i] 

[2431 

20-24 

43 

45-49 

90 

70-74 

110 

0-5 

340 

25-29 

49 

50-54 

83 

75-79 

72 

5-9 

20 

30-34 

62 

55-59 

73 

80-84 

66 

10-14 

26 

35-39 

58 

60-64 

107 

85-89 

33 

15-19 

33 

40-44 

56 

65-69 

109 

90-94 

18 

95-99 

4 

U.  S.  Mortality  Statistics,  1914,  p.  264. 


ADJUSTED   DEATH-RATES 


243 


The  Standard  Million1  will  be  taken  as  the  standard  of 
population.  It  is  necessary  to  take  an  age-grouping  which 
will  correspond  to  this,  and  find  the  number  of  persons  in 
Cambridge  in  1914  in  each  of  these  groups.  There  was  no 
census  in  Cambridge  in  1914,  but  in  1910  the  population 
was  104,839,  in  1900  it  was  91,886.  The  estimated  popu- 
lation July  1,  1914,  was  110,357.  In  1910  the  age  distri- 
bution of  the  people  of  Cambridge  was  given  by  the  census. 
It  was  as  follows  (columns  1,  2  and  3) : 

TABLE  63 
PERSONS  LESS  THAN  STATED  AGE:    CAMBRIDGE,  MASS. 


Age. 

Actual  number  of 
persons  in  1910 

Per  cent. 

Computed  number  of 
persons  in  1914. 

(1) 

(2) 

(3) 

(4) 

1 

2,323 

2.3 

2,430 

5 

10,802 

10.4 

11,500 

10 

20,273 

19.4 

21,400 

15 

29,165 

27.9 

30,800 

20      A. 

37,095 

36.4 

40,200 

25 

47,503 

46.4 

51,200 

35 

66,678 

64.6 

70,500 

45 

82,404 

79.6 

88,000 

65 

99,136 

95.6 

105,700 

100 

104,778 

99.4 

110,280 

Unknown 

61 

0.6 

77 

Total 

104,839 

100.0 

110,357 

It  may  be  fairly  assumed  that  the  percentages  of  column 
3  for  1910  apply  also  with  no  great  change  to  1914.  By 
multiplying  110,357,  therefore,  by  these  percentages  we 
get  the  following  numbers  of  persons  in  each  group  for 
1914  (column  4). 

The  figures  in  column  (4)  may  be  redistributed  in  any 


Seep.  181. 


244 


SPECIFIC  DEATH-RATES 


desired  age-grouping  as  described  on  p.  172.  In  this  way 
the  figures  in  column  (2)  of  the  following  table  were  ob- 
tained : 

TABLE  64 
ADJUSTED  DEATH-RATES  FOR  CAMBRIDGE,  MASS. 


Age-,;roup. 

Estimated 
population  in 
1914 
(approximate). 

Number  of 
deaths  in 
1914. 

Specific 
death-rate 
per  1000. 

Standard 
age  distribution 
per  1000. 

Computed 
deaths. 

(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

0-4 

11,500 

340 

29.5 

114.262 

0.380 

5-9 

9,900 

20 

2.02 

107.209 

0.217 

10-14 

9,400 

26 

2.76 

102.735 

0.284 

15-19  . 

9,400 

33 

3.51 

99.796 

0.350 

20-24 

11,000 

43 

3.91 

95.946 

0.374 

25-34 

19,200 

111 

5.78 

161.579 

0.935 

35-44 

17,400 

114 

6.53 

122.849 

0.803 

45-54 

11,600 

173 

14.9 

89.222 

1.330 

55-64 

5,800 

180 

31.1 

59.741 

1.856 

65-74 

3,100 

219 

70.6 

33.080 

2.330 

75- 

2,100 

193 

91.8 

13.581 

1.246 

Total 

110,400 

1452 

13.15 

1000.000 

13.105 

From  columns  (2)  and  (3)  the  specific  death-rates  are 
obtained  (column  4),  and  these  applied  to  the  standard 
age  distribution  (column  5)  give  the  number  of  computed 
deaths  in  each  age-group  (column  6).  Their  sum  gives 
13.1,  which  is  the  death-rate  adjusted  to  the  standard 
age  distribution.  We  have  done  all  this  work  to  get  a 
result  which  differs  but  fractionally  from  the  general,  or 
crude  death-rate,  i.e.,  13.15.  Not  worth  while?  Yes,  it 
is  if  we  are  to  use  a  death-rate  at  all.  It  was  only  because 
the  age  distribution  of  the  Cambridge  population  happened 
to  be  so  near  that  of  the  standard  million  that  the  two 
death-rates  came  so  close  together.  In  another  case  the 
result  might  be  very  different. 


ADJUSTED   DEATH-RATES 


245 


A  fair  criticism  of  this  last  computation  would  be  that 
the  age-groupings  below  age  five  and  above  middle  age  are 
too  wide,  for  it  is  in  these  groups  where  the  specific  death- 
rates  are  highest.  Dr.  Wm.  L.  Holt,  C.P.H.  (School  of 
Public  Health,  Harvard  University  and  Mass..  Inst.  of 
Tech.),  investigated  this  subject  of  grouping  and  concluded 
that  seven  properly  selected  groups  would  give  results 
which  compared  well  with  those  obtained  by  using  the 
eleven  groups  of  the  Standard  Million.  The  author  be- 
lieves that  even  five  well-chosen  groups  would  suffice,  but 
the  matter  is  one  which  needs  free  discussion.  Certainly 
something  more  convenient  than  the  Standard  Million  is 
possible. 

TABLE  65 

COMPUTED  DEATH-RATES  IN  BOSTON  AND   CAM- 
BRIDGE, 1905 

(Computations  by  Dr.  Wm.  L.  Holt) 

.    Boston. 


Adjusted  rates  per  1000. 

Age- 
group. 

Popula- 
tion. 

Deaths. 

Specific 
death-rate. 

Eleven 

Nine 

Seven 

Six 

groups. 

groups. 

groups. 

groups. 

(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

(7) 

(8) 

0-4 

52,152 

3128 

60.1 

6.850 

6.850 

6.850 

6.850 

5-9 

54,091 

253 

4.68 

0.501 

0.501  j 

10-14 
15-19 

48,694 
47,608 

157 

218 

3.22 

4.58 

0.331  I 
0.457f 

0.785  I 

1.963 

1.963 

20-24 

57,421 

380 

6.61 

0.634 

0.634J 

25-34 
35-44 

119,632 
95,946 

1070 
1081 

8.95 
11.28 

1.441 
1.388 

1.441  ) 
1.188) 

2.840 

2.840 

45-54 

58,810 

1255 

21.4 

1.910 

1.910 

1.910( 

41  op 

55-64 

33,602 

1308 

38.9 

2.325 

2.325 

2.3251 

.  Loo 

65-74 

16,711 

1213 

72.6 

2.403; 

4809 

2.403 

2.403 

75- 

6,413 

937 

146.0 

1.980J 

1.980 

1.980 

Total 

20.220 

20.636 

20.271 

20.171 

(Continued  on  next  page.) 


246 


SPECIFIC  DEATH-RATES 


Cambridge. 


Age- 

Popula- 

Deaths. 

Specific 

Adjusted  ra 

^s  per  1000. 

group. 

tion. 

death-rate. 

Eleven  groups. 

Seven  groups. 

(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

0-4 

9,088 

412 

45.3 

5.176 

5.176 

5-9 

9,096 

27 

2.96 

0.317^ 

10-14 
15-19 

8,078 
8,512 

20 
34 

2.48 
4.00 

0.255  1 
0.399  f 

1.468 

20-24 

10,789 

51 

4.72 

0.452J 

25-34 

18,671 

130 

6.97 

.125) 

2'  9^ 

35-44 

14,148 

130 

9.19 

.127  J 

.  _•  >•  > 

45-54 

9,267 

133 

14.35 

.280 

1.280 

55-64 

5,628 

165 

29.4 

.755 

1.755 

65-74 

2,864 

155 

54.1 

.790 

1.790 

75- 

1,251 

179 

143.2 

.950 

1.950 

Total 

15.626 

15.672 

Examples  of  death-rates  adjusted  to  a  standard  popu- 
lation. —  The  U.  S.  Mortality  Statistics  give  numerous 
examples  of  death-rates  adjusted  to  the  Standard  Million. 

Let  us  first  of  all  compare  Cambridge,  Mass.,  and  Chicago, 

111. 

TABLE  66 


City. 

Death-rate,  1911. 

Gross. 

Adjusted. 

(1) 

(2) 

(3) 

Cambridge,  Mass. 
Chicago,  111. 

15.2 
14.5 

15.4 
16.4 

Here  again  we  see  that  adjustment  of  the  Cambridge  rate 
changes  it  but  little,1  while  that  of  Chicago  was  increased 
by  1.9,  making  the  adjusted  rate  higher  than  that  of 
Cambridge..  Why? 

1  In  this  computation  sex  as  well  as  age  was  considered. 


EXAMPLES  OF  ADJUSTED  DEATH-RATES 


247 


In  every  instance  in  the  following  table  the  adjusted 
death-rate  exceeded  the  gross  death-rate,  the  excesses 
ranging  from  1  to  18  per  cent  and  averaging  8.4  per  .cent. 
As  would  naturally  be  expected  the  differences  were  less 
in  the  older  cities  of  the  East  than  in  the  newer  cities 
of  the  West,  but  New  York,  Pittsburgh  and  a  few  others 
with  large  numbers  of  recent  immigrants  were  exceptions 
to  this  rule.  The  following  figures  illustrate  this: 


TABLE  67 

COMPARISON  OF  GROSS  AND  ADJUSTED  DEATH-RATES 
FOR  CERTAIN  CITIES 


Death-rates  per  1000. 

City. 

Gross. 

Adjusted. 

Difference. 

.(1) 

(2) 

(3) 

(4) 

New  Haven,  Conn. 

16.7 

17.7 

1.0 

Boston,  Mass. 

17.1 

17.9 

0.8 

New  York,  N.  Y. 

15.2 

17.2 

2.0 

Pittsburgh,  Pa. 
Cleveland,  Ohio 

14.9 
13.8 

16.9 
15.3 

.       2.0 
1.5 

Chicago,  111. 

14.5 

16.4 

1.9 

Spokane,  Wash. 
Seattle,  Wash. 

11.6 

8.8 

13.7 
10.4 

2.1 

1.6 

Adjustment  to  a  standard  population  tends  to  equalize 
the  death-rates  in  different  places.  The  rural  districts  of 
New  England  contain  a  large  percentage  of  persons  of  ad- 
vanced age.  This  tends  to  cause  the  adjusted  rate  to  be 
lower  than  the  gross  rate.  Taking  figures  for  entire  states 
we  find  this  to  be  true,  as  the  following  figures  show.  In 
the  western  "states  this  difference  is  not  as  marked,  as  they 
have  not  Suffered  by  emigration  as  have  the  New  England 
States. 


248 


SPECIFIC  DEATH-RATES 


TABLE  68 

COMPARISON  OF  GROSS  AND  ADJUSTED  DEATH-RATES 
FOR  CERTAIN  STATES 


Death-rates  per  1000. 

State 

Gross. 

Adjusted. 

Difference. 

(1) 

(2) 

(3) 

(4) 

Massachusetts 

15.3 

15.0 

-0.3 

New  Hampshire 

17.1 

14.2 

-2.9 

Maine 

16.1 

13.0 

-3.1 

Connecticut 

15.4 

14.8 

-0.6 

Indiana 

12.9 

12.3 

-0.6 

Kentucky 

13.2 

13.4 

0.2 

Michigan 

13.2 

12.4 

-0.8 

Minnesota 

10.5 

10.8 

0.3 

Missouri 

13.1 

13.1 

0.0 

Montana 

10.2 

11.6 

1.4 

The   following  figures   show  the   relation  between  the 
crude  and  adjusted  death-rates  for  various  countries: 


ADJUSTMENT  FOR  RACIAL  DIFFERENCES        249 


TABLE  69 

COMPARISON  OF  GROSS  AND  ADJUSTED  DEATH-RATES 
FOR  CERTAIN  COUNTRIES 


Ratio  of 

Death-rates  per  1000. 

adjusted 

Country. 

Year. 

rate 
to  that  of 

. 

Gross. 

Adjusted. 

Difference. 

England 
and  Wales. 

(1) 

(2) 

(3) 

(4) 

(5) 

x    (6) 

Russia 

1896-1898 

32.80 

28.61 

-4.19 

166.7 

Spain 

1900-1902 

27.63 

26.53 

-1.10 

154.6 

Austria 

1899-1901 

24.83 

23.12 

-1.71     . 

134.7 

Italy 

1900-1902 

22.72 

20.23 

-2.49 

117.9 

Germany 
U.  S.  (Registra- 

1901 
1900 

20.84 
17.55 

19.52 
18.05 

-1.32 
0.50 

113.8 
105.2 

tion  area) 

Scotland 

1900-1902 

17.91 

17.61 

-0.30 

102.6 

France 

1900-1902 

20.80 

17.50 

-3.30 

102.0 

England  &  Wales 
Switzerland 

1900-1902 
1899-1901 

17.16 
18.22 

17.16 
16.86 

0.00 
-1.36 

100.0 
98.3 

Belgium 

1899-1901 

18.53 

16.78 

-1.75 

97.8 

Ireland 

1900-1902 

18.27 

16.59 

-1.68 

96.7 

Netherlands 

189&-1900 

17.32 

15.40 

-1.92 

89.7 

Sweden 

1899-1901 

16.78 

13.88 

-2.90 

80.9 

New  South  Wales 

1900-1902 

11.72 

13.10 

1.38 

76.3 

Victoria 

1900-1902 

13.12 

13.08 

-0.04 

76.2 

South  Australia 

1900-1902 

11.02 

11.73 

0.71 

68.4 

Adjustment  for  racial  differences.  —  In  certain  parts 
of  the  United  States,  especially  in  the  South,  the  crude 
death-rates  are  absolutely  useless  for  purposes  of  com- 
parison unless  allowance  is  made  for  the  number  of  colored 
persons  at  different  ages.  The  specific  death-rates  for  col- 
ored persons  are  higher  at  all  ages  than  for  white  persons, 
as  the  following  figures  for  the  U.  S.  registration  states  in 
1900  show: 


250 


SPECIFIC   DEATH-RATES 


TABLE  70 

COMPARISON  OF  SPECIFIC  DEATH-RATES  FOR  WHITE 
AND  COLORED  PERSONS 


Death-rates  per  1000  (exclusive 
of  still-births). 

Ratio  of  colored 

Age-group  (both  sexes). 

to  white  death- 

rate. 

Native  white. 

Colored. 

(1) 

(2) 

(3) 

(4) 

0-4 

49.1 

106.4 

2.17 

5-9 

4.5 

8.9 

1.98 

10-14 

2.9 

9.0 

3.10 

15-19 

4.7 

11.4 

2.43 

20-24 

6.8 

11.6 

.71 

'    25-34 

8.2 

12.2 

.49 

35-44 

9.6 

15.0 

.56 

45-54  . 

12.7 

24.5 

.93 

55-64 

22.6 

42.5 

.88 

65-74 

50.4 

69.5 

.38 

75 

138.5 

143.3 

.03 

Crude  death-rate 

16.5 

25.0 

1.52 

The  following  figures  for  the  cities  of  Washington,  Balti- 
more and  New  Orleans  show  the  necessity  of  taking  into  ac- 
count these  striking  differences  between  the  white  and  colored 
people: 


DEATH-RATES  FOR  PARTICULAR  DISEASES      251 


TABLE  71 

ADJUSTED  DEATH-RATES  FOR  CITIES  HAVING  LARGE 
COLORED  POPULATIONS 


Death-rates  per  1000  (both  sexes),  1911. 

Gross. 

Adjusted. 

Difference. 

(1) 

(2) 

(3) 

(4) 

Washington,  D.  C. 
White 
Colored 
Total 

15.5 
26.6 
18.7 

14.6 
30.5 
18.9 

-0.9 
3.9 
0.2 

Baltimore,  Md. 
White 
Colored 
Total 

16.2 
30.9 
18.4 

16.7 
35.4 
19.4 

0.5 
4.5 
1.0 

New  Orleans,  La. 
White 
Colored 
Total 

16.6 
31.2 
20.4 

17.5 
34.0 

21.8 

0.9 
2.8 
1.4 

Death-rates  for  particular  diseases.  —  Death-rates  for 
particular  diseases  are  computed  in  the  same  way  as  other 
specific  death-rates.  The  numerator  of  the  ratio  is  limited 
to  the  disease  in  question.  The  denominator  may  be  the 
entire  population,  or  it  may  be  confined  to  some  specific 
part  of  it.  In  order  to  avoid  the  use  of  too  many  decimals 
it  is  well  to  express  the  death-rates  for  particular  diseases  as 
so  many  per  100,000  instead  of  so  many  per  1000.  This 
practice  is  becoming  universal.  The  use  of  10,000  as  a 
base  should  be  avoided. 

If  all  of  the  deaths  from  typhoid  fever  be  compared  with 
the  total  mid-year  population,  we  have  the  general  typhoid 
fever  death-rate  of  the  place.  General  rates  for  particular 
diseases  are  much  used  and  have  practical  value.  Specific 


252  SPECIFIC  DEATH-RATES 

rates  in  which  deaths  from  typhoid  fever  in  a  given  age- 
group  are  compared  with  the  population  in  the  same  age- 
group  are  sometimes  computed,  but  are  useful  only  when 
the  numbers  involved  are  large. 

Special  death-rates.  —  In  epidemiological  studies  it  is 
necessary  to  compute  death-rates  in  all  sorts  of  ways,  to 
separate  the  people  into  classes  according  to  where  and  how 
they  live,  according  to  their  occupation  or  their  exposure 
to  certain  risks.  This  causes  us  to  deal  with  many  special 
rates. 

In  studying  birth  statistics  we  may  find  the  general 
birth-rate,  by  taking  the  ratio  between  the  number  of 
births  and  the  total  population.  But  we  may  also  desire 
to  find  the  ratio  between  births  and  women  of  child- 
bearing  age,  or  between  births  and  married  women  of 
child-bearing  age. 

In  interpreting  all  of  these  many  sorts  of  rates  and  ratios 
the  principles  already  outlined  hold  good.  We  must  see 
that  the  data  compared  are  logically  comparable,  that  there 
are  no  concealed  classifications  and  that  the  rules  of  pre- 
cision are  not  violated. 


EXERCISES  AND    QUESTIONS 

1.  Are  the  changes  in  age-composition  from  decade  to  decade  in 
Massachusetts  sufficient  to  explain  a  considerable  part  of  the  falling 
general  death-rate  of  the  state,  assuming  the  specific  death-rates  by 
ages  to  remain  constant? 

2.  'Compute  the  specific  death-rates  by  sex  and  age-groups  for  three 
Massachusetts  cities  for  1910,  obtaining  data  from  the  census  and 
registration  reports. 

3.  Compare  the  specific  death-rates  by  age-groups  for  white  and 
colored  persons  in  some  southern  city  for  some  selected  year. 

4.  Adjust  the  death-rate  of  some  western  city  in  1910  to  the  Swedish 
standard  of  population. 


EXERCISES  AND  QUESTIONS  253 

5.  Repeat  this  computation  using  the  standard  million  as  a  basis  of 
adjustment. 

6.  Select  from  the  Mortality  Reports  examples  of  the  need  of  adjust- 
ment of  death-rates  of  cities  for  purposes  of  comparison. 

7.  Adjust  the  death-rates  of  some  selected  city  to  the  basis  of  the 
Standard  Million  for  1915,  1910,  1905,  1900  and  as  far  back  as  record 
can  be  obtained. 


CHAPTER  VIII 
CAUSES   OF  DEATH 

Nosography.  —  The  description  and  systematic  classifi- 
cation of  disease  is  called  nosography.  The  word  is  derived 
from  the  Greek  word  nosos,  which  means  sickness,  or  disease. 
(The  word  is  pronounced  noss'ography,  not  noze-ography.) 

Nosology.  —  The  science  of  classifying  disease  is  similarly 
called  nosology. 

The  purpose  of  nosology.  —  At  one  time  it  was  thought 
that  a  knowledge  of  nosology  was  necessary  for  the  practical 
treatment  of  disease.  Many  systems  were  proposed  and 
abandoned.  Today  the  idea  has  few,  if  any,  supporters. 

Nosology. is  of  great  importance  as  one  of  the  foundation 
stones  of  our  modern  structure  of  vital  statistics.  Without 
uniform  definitions  of  disease  which  furnish  us  with  adequate 
statistical  units  our  statistics  would  be  worthless.  It  is  because 
of  changes  in  our  definitions  of  disease  that  we  fall  into  so 
many  errors  in  comparing  past  conditions  with  those  of  the 
present  day.  Such  changes  are  inevitable  as  medical  science 
advances,  but  they  ought  to  be  universally  recognized  when 
they  are  made. 

Dr.  William  Farr  was  one  of  the  first  to  recognize  the 
importance  of  "  statistical  nosology." 

History  of  nosography.  —  Nosography  emerged  from  its 
former  chaotic  condition  in  1893  when  the  use  of  the  Inter- 
national Classification  of  Diseases  and  Causes  of  Death  was 
begun.  This  was  due  chiefly  to  the  labors  of  Dr.  Jacques 
Bertillon  of  France. 

254 


INTERNATIONAL  LIST  OF  THE  CAUSES  OF  DEATH     255 

In  1853  Dr.  William  Fair  and  Dr.  Marc  d'Espine,  of 
Geneva,  had  been  selected  by  the  First  Statistical  Congress, 
which  met  at  Brussels,  to  present  a  report  on  the  subject. 
The  list  of  diseases  reported  by  them  was  adopted  in  Paris  in 
1855,  in  Vienna  in  1857,  and  was  translated  into  six  languages. 
It  was  revised  several  times  between  1864  and  1886.  In  1893 
the  International  Statistical  Institute,  the  successor  of  the 
Statistical  Congress,  met  in  Chicago  and  adopted  this  list 
with  some  changes.  Provision  was  made  for  decennial 
revisions  by  an  International  Commission,  and  such  revisions 
were  made  in  Paris  in  1900  and  again  in  1909,  the  latter  a 
year  earlier  in  order  that  the  new  list  might  be  used  in  the 
censuses  of  1910.  The  present  list  is  intended  to  stand  un- 
changed until  1919.  In  1898  the  International  List  was 
endorsed  by  the  American  Public  Health  Association.  Eng- 
land adopted  the  list  in  1911.  It  is  used  by  all  English  and 
Spanish  speaking  countries,  but  it  is  not  yet  universal.  A 
few  of  our  own  states"  do  not  follow  it  exactly,  namely: 
Alabama,  New  Hampshire,  New  Mexico,  Rhode  Island  and 
West  Virginia. 

International  list  of  the  causes  of  death.  —  In  1911  the 
U .  S.  Bureau  of  the  Census  published  a  Manual  of  297  pages, 
being  a  revision  of  a  former  manual  published  in  1902.  This 
list  is  the  present  standard  for  the  United  States  and  has 
come  to  be  almost  universally  used.  This  manual  is  very 
complete.  It  gives  the  standard  list  of  the  causes  of  death, 
with  synonyms,  and  is  indexed  alphabetically  as  well  as 
according  to  the  chosen  classification. 

The  Bureau  of  the  Census  also  publishes  a  Physician's 
Pocket  Reference  to  the  International  List  of  the  Causes  of 
Death,  which  can  be  obtained  without  charge  by  anyone  who 
makes  request  of  the  Director  of  the  Census,  Washington, 
D.  C.  This  is  a  small  pamphlet  of  28  pages,  vest  pocket 


256  CAUSES  OF  DEATH 

Classification  of  diseases  in  1850.  —  Dr.  Fair  classified 
diseases  as  follows: 

CLASS  I.  EPIDEMIC,  ENDEMIC  and  CONTAGIOUS  diseases  (Zymotici). 

Order  1 .   Miasmatic  diseases,  —  small-pox,  ague,  etc. 

Order  2.   Enthenic  diseases,  —  syphilis,  glanders. 

Order  3.   Dietetic  diseases,  —  scurvy,  ergotism. 

Order  4.   Parasitic  diseases. 
CLASS  II.  CONSTITUTIONAL  DISEASES  (Cachectici) . 

Order  1.   Diathetic  diseases,  —  gout,  dropsy,  cancer,  etc. 

Order  2.    Tubercular  diseases,  —  scrofula,  consumption. 
CLASS  III.  LOCAL  DISEASES  (Monorganici). 

Order  1.   Diseases  of  the  brain. 

Order  2.   Diseases  of  the  circulation. 

Order  3.   Diseases  of  respiration. 

Order  4.   Diseases  of  digestion. 

Order  5.   Diseases  of  the  urinary  system. 

Order  6.   Diseases  of  reproduction. 

Order  7.   Diseases  of  locomo'ive  system.    • 

Order  8.  Diseases  of  integumentary  system. 
CLASS  IV.  DEVELOPMENTAL  DISEASES  (Metamorphici). 
CLASS  V.  VIOLENT  DEATHS  OR  DISEASES  (Thanatici). 

It  is  extremely  interesting  to  study  this  list  in  detail  as 
given  in  the  16th  Annual  Report  of  the  Registrar  General 
of  England,  Appendix,  pp.  71-79. 

Present  classification.  —  The  list  recognizes  189  causes 
of  death,  which  are  divided  into  fourteen  classes.  It  is  not 
claimed  that  these  are  all  of  the  possible  causes.  For  con- 
venience of  reference  and  tabulation  each  of  these  diseases 
is  given  a  number.  The  following  Is  the  list  as  given  in  the 
Physician's  Pocket  Reference.  It  is  recommended  that  only 
the  names  printed  in  heavy  type  be  used.  The  terms  in 
italics  are  indefinite  or  otherwise  undesirable.  An  abridged 
list  of  causes  of  death  useful  for  annual  reports  of  health 
departments  may  be  found  on  page 


PRESENT  CLASSIFICATION  257 

INTERNATIONAL  LIST  OF  CAUSES  OF  DEATH 

(I.  —  GENERAL  DISEASES) 

1.  Typhoid  fever. 

2.  Typhus  fever. 

3.  Relapsing  fever.     [Insert  "(spirillum)."] 

4.  Malaria. 

5.  Smallpox. 

6.  Measles. 

7.  Scarlet  fever. 

8.  Whooping  cough. 

9.  Diphtheria  and  croup. 

10.  Influenza. 

11.  Miliary  fever.     [True  Febris  miliaris  only.] 

12.  Asiatic  cholera. 

13.  Cholera  nostras. 

14.  Dysentery.     [Amebic?      Bacillary?      Do    not    report    ordinary 

diarrhea  and  enteritis  (104,  105)  as  dysentery.] 

15.  Plague. 

16.  Yellow  fever. 

17.  Leprosy. 

18.  Erysipelas.     [State  also  cause;  see  Class  XIII.] 

19.  Other  epidemic  diseases: 

Mumps, 

German  measles, 

Chicken-pox, 

Rocky  Mountain  spotted  (tick)  fever, 

Glandular  fever,  etc. 

20.  Purulent  infection  and  septicemia.    [State  also  cause;  see  Classes 

VII  and  XIII  especially.] 

21.  Glanders. 

22.  Anthrax. 

23.  Rabies. 

24.  Tetanus.     [State  also  cause;  see  Class  XIII. J 

25.  Mycoses.     [Specify,  as  Actinomycosis  of  lung,  etc.] 

26.  Pellagra. 

27.  Beriberi. 

28.  Tuberculosis  of  the  lungs. 

29.  Acute  miliary  tuberculosis. 

30.  Tuberculous  meningitis. 


258  CAUSES  OF  DEATH 

31.  Abdominal  tuberculosis. 

32.  Pott's  disease.     [Preferably  Tuberculosis  of  spine.] 

3$.  White  swellings.     [Preferably  Tuberculosis  of  —   —  joint.] 

34.  Tuberculosis  of  other  organs.     [Specify  organ.] 

35.  Disseminated  tuberculosis.     [Specify  organs  affected.] 

36.  Rickets. 
-  37.  Syphilis. 

38."  Gonococcus  infection. 

39.  Cancer  *  of  the  buccal  cavity.     [State  part.] 

40.  Cancer  *  of  the  stomach,  liver. 

41.  Cancer  l  of  the  peritoneum,  intestines,  rectum. 

42.  Cancer  1  of  the  female  genital  organs.     [State  organ.] 

43.  Cancer  l  of  the  breast. 

44.  Cancer  1  of  the  skin.     [State  part.] 

45.  Cancer  x  of  other  or  unspecified  organs.     [State  organ.] 

46.  Other  tumors  (tumors  of  the  female  genital  organs  exoepted.) 

[Name  kind  of  tumor  and  organ  affected.     Malignant?] 

47.  Acute  articular  rheumatism.     [Always  state  "  rheumatism  "  as 

acute  or  chronic.] 

48.  Chronic  rheumatism  [preferably  Arthritis  deformans]  and  gout. 

49.  Scurvy. 

50.  Diabetes.     [Diabetes  mellitus.] 

51.  Exophthalmic  goiter. 

52.  Addison's  disease. 

53.  Leukemia. 

54.  Anemia,  chlorosis.     [State  form  or  cause.     Pernicious?] 

55.  Other  general  diseases: 

Diabetes  insipidus, 
Purpura  haemorrhagica,  etc. 

56.  Alcoholism  (acute  or  chronic). 

57.  Chronic  lead  poisoning.     [State  cause.     Occupational?] 

58.  Other  chronic  occupational  poisonings.      [State  exact  name  of 

poison,  whether  the  poisoning  was  chronic  and  due  to  oc- 
cupation, and  also  please  be  particularly  careful  to  see  that 
the  Special  Occupation  and  Industry  are  fully  stated.  If 

1  "  Cancer  and  other  malignant  tumors."     Preferably  reported  as 

Carcinoma  of ,  Sarcoma  of ,  Epithelioma  of ,  etc.,  stating 

the  exact  nature  of  the  neoplasm  and  the  organ  or  part  of  the  body  first 
affected. 


PRESENT  CLASSIFICATION 


259 


the  occupation  stated  on  the  certificate  is  not  that  in  which 
the  poisoning  occurred,  add  the  latter  in  connection  with  the 
statement  jof  cause  of  death,  e.g.,  u  Chronic  occupational 
phosphorus  necrosis  (dipper,  match  factory,  white  phos- 
phorus)." Give  full  details,  including  pathologic  conditions 
contributory  to  death.  Following  is  a  List  of  Industrial 
Poisons  (Butt.  Bureau  of  Labor,  May,  1912)  to  which  the 
attention  of  physicians  practicing  in  industrial  communities 
should  be  especially  directed: 


Acetaldehyde, 

Acridine, 

Acrolein, 

Ammonia, 

Amyl  acetate, 

Amyl  alcohol, 

Aniline, 

Aniline  dyestuffs  [name], 

Antimony  compounds  [name], 

Arsenic  compounds  [name], 

Arseniureted  hydrogen, 

Benzine, 

Benzol, 

Carbon  dioxide, 

Carbon  disulphide, 

Carbon  monoxide  (coal  vapor,  il- 
luminating water  gas,  producer 
gas), 

Chloride  of  lime, 

Chlorine, 

Chlorodinitrobenzol, 

Chloronitrobenzol, 

Chromium  compounds  [name], 

Cyanogen  compounds  [name], 

Diazomethane, 

Dimethyl  sulphate, 

Dinitrobenzol, 

Formaldehyde, 


Hydrochloric  acid, 

Hydrofluoric  acid, 

Lead  (57), 

Manganese  dioxide, 

Mercury, 

Methyl  alcohol, 

Methyl  bromide, 

Nitraniline, 

Nitrobenzol, 

Nitroglycerin, 

Nitronaphthalene, 

Nitrous  gases, 

Oxalic  acid, 

Petroleum, 

Phenol, 

Phenylhydrazine, 

Phosgene, 

Phosphorus  (yellow  or  white), 

Phosphorus  sesquisulphide, 

Phosphureted  hydrogen, 

Picric  acid, 

Pyridine, 

Sulphur  chloride, 

Sulphur  dioxide, 

Sulphureted  hydrogen, 

Sulphuric  acid, 

Tar, 

Turpentine  oil. 


Not  all  substances  in  the  preceding  list  are  likely  to  be  reported 
as  causes  of  death,  but  the  physician  should  be  familiar  with  it  in 
order  to  recognize,  and  to  report,  if  required,  cases  of  illness,  and 


260  CAUSES  OF  DEATH 

should  also  be  on  the  alert  to  discover  new  forms  of  industrial  poi- 
soning not  heretofore  recognized.  In  the  Bulletin  cited  full  details 
may  be  found  as  to  the  branches  of  industry  in  which  the  poisoning 
occurs,  mode  of  entrance  into  the  body,  and  the  symptoms  of  poi- 
soning. Attention  should  also  be  called  to  industrial  infection,  e.g., 
Anthrax  (22),  and  the  influence  of  gases  and  vapors,  dust,  or  unhygienic 
industrial  environment. 

59.  Other  chronic  poisonings: 

Chronic  morphinism, 
Chronic  cocainism,  etc. 

(II.  —  DISEASES  OF  THE  NERVOUS  SYSTEM  AND  OF  THE  ORGANS  OF 
SPECIAL  SENSE) 

60.  Encephalitis. 

61.  Meningitis: 

Cerebrospinal  fever  or  Epidemic  cerebrospinal  meningitis, 
Simple  meningitis.     [State  cause.] 

62.  Locomotor  ataxia. 

63.  Other  diseases  of  the  spinal  cord: 

Acute  anterior  poliomyelitis, 
Paralysis  agitans, 
Chronic  spinal  muscular  atrophy, 
Primary  lateral  sclerosis  of  spinal  cord, 
Syringomyelia,  etc. 

64.  Cerebral  hemorrhage,  apoplexy. 

65.  Softening  of  the  brain.     [State  cause.] 

66.  Paralysis  without  specified  cause.     [State  form  or  cause.] 

67.  General  paralysis  of  the  insane. 

68.  Other  forms  of  mental  alienation.    [Name  disease  causing  death. 

Form  of  insanity  should  be  named  as  CONTRIBUTORY  CAUSE 
only,  unless  it  is  actually  the  disease  causing  death.] 

69.  Epilepsy. 

70.  Convulsions  (nonpuerperal) .     [State  cause.] 

71.  Convulsions  of  infants.     [State  .cause.] 

72.  Chorea. 

73.  Neuralgia  and  neuritis.     [State  cause.] 

74.  Other  diseases  of  the  nervous  system.     [Name  the  disease.] 

75.  Diseases  of  the  eyes  and  their  annexa.     [Name  the  disease.] 

76.  Diseases  of  the  ears.     [Name  the  disease.] 


PRESENT  CLASSIFICATION  261 

(III.  —  DISEASES  OF  THE  .CIRCULATORY  SYSTEM) 

77.  Pericarditis.     [Acute  or  chronic;  rheumatic  (47),  etc.] 

78.  Acute  endocarditis.     [Cause?    Always  report  "  endocarditis  "  or 

"  myocarditis  "  as  acute  or  chronic.     Do  not  report  when 
mere  terminal  condition.] 
Acute  myocarditis. 

79.  Organic  diseases  of  the  heart:   [Name  the  disease.] 

Chronic  valvular  disease,  [Name  the  disease.] 
Aortic  insufficiency, 

Chronic  endocarditis,  [See  note  on  (78).] 
Chronic  myocarditis,  [See  note  on  (78).] 
Fatty  degeneration  of  heart,  etc. 

80.  Angina  pectoris. 

81.  Diseases  of  the  arteries,  atheroma,  aneurism,  etc. 

82.  Embolism  and  thrombosis.     [State  organ.     Puerperal  (139)?] 

83.  Diseases  of  the  veins  (varices,  hemorrhoids,  phlebitis,  etc.). 

84.  Diseases  of  the  lymphatic  system  (lymphangitis,  etc.).     [Cause? 

Puerperal?] 

85.  Hemorrhage;  other  diseases  of  the  circulatory  system.    [Cause? 
Pulmonary  hemorrhage  from  Tuberculosis  of  lungs  (28)?     Puer- 
peral?] 

(IV.  —  DISEASES  OF  THE  RESPIRATORY  SYSTEM) 

86.  Diseases  of  the  nasal  fossae.     [Name  disease.] 

87.  Diseases  of  the  larynx.     [Name  disease.     Diphtheritic?] 

88.  Diseases  of  the  thyroid  body.     [Name  disease.] 

89.  Acute  bronchitis.     )  [Always  state  as  acute  or  chronic.    Was  it 

90.  Chronic  bronchitis.  J       tuberculous?] 

91.  Bronchopneumonia.     [If  secondary,  give  primary  cause.] 

92.  Pneumonia.     [If  lobar,  report  as  Lobar  pneumonia.] 

93.  Pleurisy.     [Cause?     If  tuberculous,  so  report  (28).] 

94.  Pulmonary  congestion,  pulmonary  apoplexy.     [Cause?] 

95.  Gangrene  of  the  lung. 

96.  Asthma.     [Tuberculosis?] 

97.  Pulmonary  emphysema. 

98.  Other  diseases  of  the  respiratory  system  (tuberculosis  excepted). 

.  [Such  indefinite  returns  as  "  Lung  trouble,"  "  Pulmonary  hem- 
orrhage," etc.,  compiled  here,  vitiate  statistics.  Tuberculosis 
of  lungs  (28)?  Name  the  disease.] 


262  CAUSES  OF  DEATH 

(V.  —  DISEASES  OF  THE  DIGESTIVE  SYSTEM) 

99.   Diseases  of  the  mouth  and  annexa.     [Name  disease.] 

100.  Diseases    of    the    pharynx.      [Name    disease.      Diphtheritic?] 

Streptococcus  sore  throat. 

101.  Diseases  of  the  esophagus.     [Name  disease.] 

102.  Ulcer  of  the  stomach. 

103.  Other  diseases    of    the    stomach    (cancer    excepted).     [Name 

disease.  Avoid  such  indefinite  terms  as  "  Stomach  trouble " 
"  Dyspepsia,1'  "  Indigestion,"  "  Gastritis,"  etc.,  when  used 
vaguely.] 

104.  Diarrhea  and  enteritis  (under  2  years). 

105.  Diarrhea  and  enteritis  (2  years  and  over). 

106.  Ankylostomiasis.     [Better,  for   the  United  States,  Hookworm 

disease  or  Uncinariasis.] 

107.  Intestinal  parasites.     [Name  species.] 

108.  Appendicitis  and  typhlitis. 

109.  Hernia,  intestinal  obstruction.     [State  form  and  whether  stran- 

gulated.] 

Strangulated  inguinal  hernia  (operation), 

Intussusception, 

Volvulus,  etc. 

110.  Other  diseases  of  the  intestines.     [Name  disease.] 

111.  Acute  yellow  atrophy  of  the  liver. 

112.  Hydatid  tumor  of  the  liver.  ' 

113.  Cirrhosis  of  the  liver. 

114.  Biliary  calculi. 

115.  Other  diseases  of  the  liver.     ["  Liver  complaint  "  is  not  a  satis- 

factory return.] 

116.  Diseases  of  the  spleen.     [Name  disease.] 

117.  Simple  peritonitis  (nonpuerperal).     [Give  cause.] 

118.  Other  diseases  of  the  digestive  system  (cancer  and  tuberculosis 

excepted).     [Name  disease.] 

(VI.  —  NONVENEREAL  DISEASES   OF  THE   GENITO-URINARY   SYSTEM 
AND  ANNEXA) 

119.  Acute  nephritis.     [State  primary  cause,  especially  Scarlet  fever, 

etc.     Always  state  "  nephritis  "  as  acute  or  chronic.] 

120.  Bright's  disease.    [Better,  Chronic  interstitial  nephritis,  Chronic 

parenchymatous  nephritis,  etc.  Never  report  mere  names  of 
symptoms,  as  "  Uremia,"  "  Uremic  coma,"  etc.  See  also 
note  on  (119).] 


PRESENT  CLASSIFICATION  263 

121.  Chyluria. 

122.  Other  diseases  of  the  kidneys  and  annexa.     [Name  disease.] 

123.  Calculi  of  the  urinary  passages.     [Name  bladder,  kidney.] 

124.  Diseases  of  the  bladder.     [Name  disease.] 

Cystitis.     [Cause?] 

125.  Diseases  of  the  urethra,  urinary  abscess,  etc.     [Name  disease. 

Gonorrheal  (38)?] 

126.  Diseases  of  the  prostate.     [Name  disease.] 

127.  Nonvenereal  diseases  of  the  male  genital  organs.     [Name  disease.] 

128.  Uterine  hemorrhage  (nonpuerperal).     [Cause?] 

129.  Uterine  tumor  (noncancerous).     [State  kind.] 

130.  Other  diseases  of  the  uterus.     [Name  disease.] 

Endometritis.     [Cause?     Puerperal  (137)?] 

131.  Cysts  and  other  tumors  of  the  ovary.     [State  kind.] 

132.  Salpingitis  and  other  diseases  of  the  female  genital  organs. 

[Name  disease.     Gonorrheal  (38)?     Puerperal  (137)?] 

133.  Nonpuerperal  diseases  of  the  breast  (cancer  excep ted).     [Name 

disease.] 

(VII.  — THE  PUERPERAL  STATE) 

NOTE.  —  The  term  puerperal  is  intended  to  include  pregnancy, 
parturition,  and  lactation.  Whenever  parturition  or  miscarriage  has 
occurred  within  one  month  before  the  death  of  the  patient,  the  fact 
should  be  certified,  even  though  childbirth  may  not  have  contributed 
to  the  fatal  issue.  Whenever  a  woman  of  childbearing  age,  especially 
if  married,  is  reported  to  have  died  from  a  disease  which  might  have  been 
puerperal,  the  local  registrar  should  require  an  explicit  statement  from  the 
reporting  physician  as  to  whether  the  disease  was  or  was  not  puerperal 
in  character.  The  following  diseases  and  symptoms  are  of  this  class: 
Abscess  of  the  breast,  Metroperitonitis, 

Albuminuria,  Metrorrhagia, 

Cellulitis,  Nephritis, 

Coma,  Pelviperitonitis, 

Convulsions,  Peritonitis, 

Eclampsia,  Phlegmasia  alba  dolens, 

Embolism,  Phlebitis, 

Endometritis,  Pyemia, 

Gastritis,  Septicemia, 

Hemmorrhage  (uterine  or  Sudden  death, 

unqualified),  Tetanus, 

Lymphangitis,  Thrombosis, 

Metritis,  Uremia. 


264  CAUSES  OF  DEATH 

Physicians  are  requested  always  to  write  Puerperal  before  the  above 
terms  and  others  that  might  be  puerperal  in  character,  or  to  add  in 
parentheses  (Not  puerperal),  so  that  there  may  be  no  possibility  of  error 
in  the  compilation  of  the  mortality  statistics;  also  to  respond  to  the 
requests  of  the  local  registrars  for  additional  information  when,  inad- 
vertently, the  desired  data  are  omitted.  The  value  of  such  statistics 
can  be  greatly  improved  by  cordial  cooperation  between  the  medical 
professiorijand  the  registration  officials.  If  a  physician  will  not  write 
the  true  statement  of  puerperal  character  on  the  certificate,  he  may 
privately  communicate  that  fact  to  the  local  or  state  registrar,  or  write 
the  number  of  the  International  List  under  which  the  death  should  be 
compiled,  e.g.,  "  Peritonitis  (137)." 

134.  Accidents  ]  of  pregnancy:   [Name  the  condition.] 

Abortion,  [Term  not  used  in  invidious  sense;  Criminal  abor- 
tion should  be  so  specified  (184).] 
Miscarriage. 
Ectopic  gestation. 
Tubal  pregnancy,  etc. 

135.  Puerperal  hemorrhage. 

136.  Other  accidents  -  of  labor:  [Name  the  condition.] 

Caesarean  section, 

Forceps  application, 

Breech  presentation, 

Symphyseotomy, 

Difficult  labor, 

Rupture  of  uterus  in  labor,  etc. 

137.  Puerperal  septicemia. 

138.  Puerperal  albuminuria  and  convulsions. 

139.  Puerperal  phlegmasia  alba  dolens,  embolus,  sudden  death. 

140.  Following  childbirth  (not  otherwise  defined).     [Define.] 

141.  Puerperal  diseases  of  the  breast.     [Name  disease.] 

(VIII.  —  DISEASES  OF  THE  SKIN  AND  CELLULAR  TISSUE) 

142.  Gangrene.     [State  part  affected,  Diabetic  (50),  etc.] 

143.  Furuncle. 

144.  Acute  abscess.     [Name  part  affected,  nature,  or  cause.] 

145.  Other  diseases  of  the  skin  and  annexa.     [Name  disease.] 

1  In  the  sense  of  conditions  or  operations  dependent  upon  pregnancy 
or  labor,  not  "  accidents  "  from  external  causes. 

2  In  the  sense  of  conditions  or  operations  dependent  upon  pregnancy 
or  labor,  not  "  accidents  "  from  external  causes. 


PRESENT  CLASSIFICATION  265 

(IX.  —  DISEASES  OF  THE  BONES  AND  OF  THE  ORGANS  OF 
LOCOMOTION) 

146.  Diseases  of  the  bones  (tuberculosis  excepted):  [Name  disease.] 

Osteoperiostitis,  [Give  cause.] 

Osteomyelitis, 

Necrosis,  [Give  cause.] 

Mastoiditis,  etc.     [Following  Otitis  media  (76)?] 

147.  Diseases  of  the  joints  (tuberculosis  and  rheumatism  excepted). 

[Name  disease;  always  specify  Acute  articular  rheumatism 
(47),  Arthritis  deformans  (48),  Tuberculosis  of  —  joint  (33), 
etc.,  when  cause  is  known.] 

148.  Amputations.    [Name  disease  or  injury  requiring  amputation, 

thus  permitting  proper  assignment  elsewhere.] 

149.  Other  diseases  of  the  organs  of  locomotion.     [Name  disease.] 

(X.  —  MALFORMATIONS) 

150.  Congenital  malformations  (stillbirths  not  included):   [Do  not 

include  Acquired  hydrocephalus  (74)  or  Tuberculous  hydro- 
cephalus  (Tuberculous  meningitis)  (30)  under  this  head.) 

Congenital  hydrocephalus, 

Congenital  malformation  of  heart, 

Spina  binda,  etc.   ' 

(XI.  —  DISEASES  OF  EARLY  INFANCY) 

151.  Congenital  debility,  icterus,  and  sclerema:  [Give  cause  of  debility.] 

Premature  birth, 
Atrophy,  [Give  cause.] 
Marasmus?  [Give  cause.] 
Inanition,  etc.  [Give  cause.] 

152.  Other  diseases  peculiar  to  early  infancy: 

Umbilical  hemorrhage, 

Atelectasis, 

Injury  by  forceps  at  birth,  etc. 

153.  Lack  of  care. 

(XII.  —  OLD  AGE) 

154.  Senility.     [Name  the  disease  causing  the  death  of   the  old 

person.] 


266  CAUSES  OF  DEATH 

(XIII.  —  AFFECTIONS  PRODUCED  BY  EXTERNAL  CAUSES) 

NOTE.  —  Coroners,  medical  examiners,  and  physicians  who  certify 
to  deaths  from  violent  causes,  should  always  clearly  indicate  the  funda- 
mental distinction  of  whether  a  death  was  due  to  Accident,  Suicide,  or 
Homicide;  and  then  state  the  Means  or  instrument  of  death.  The 
qualification  "  probably  "  may  be  added  when  necessary. 

155.  Suicide  by  poison.     [Name  poison.] 

156.  Suicide  by  asphyxia.     [Name  means  of  death.] 

157.  Suicide  by  hanging  or  strangulation.     [Name  means  of  stran- 

gulation.] 

158.  Suicide  by  drowning. 

159.  Suicide  by  firearms. 

160.  Suicide  by  cutting  or  piercing  instruments.     [Name  instrument.] 

161.  Suicide  by  jumping  from  high  places.     [Name  place.] 

162.  Suicide  by  crushing.     [Name  means.] 

163.  Other  suicides.     [Name  means.] 

164.  Poisoning  by  food.     [Name  kind  of  food.] 

165.  Other  acute  poisonings.     [Name  poison;  specify  Accidental.] 

166.  Conflagration.     [State  fully,  as  Jumped  from  Window  of  burning 

dwelling,  Smothered  —  burning  of  theater,  Forest  fire,  etc.] 

167.  Burns  (conflagration  excepted).     [Includes  Scalding.] 

168.  Absorption  of  deleterious  gases  (conflagration  excepted) : 

Asphyxia  by  illuminating  gas  (accidental), 
Inhalation  of  -   —  (accidental),  [Name  gas.] 
Asphyxia  (accidental),  [Name  gas.] 
Suffocation  (accidental),  etc.  [Name  gas.] 

169.  Accidental  drowning. 

170.  Traumatism  by  firearms.     [Specify  Accidental.] 

171.  Traumatism  by  cutting  or  piercing  instruments.    [Name  instru- 

ment.    Specify  Accidental.] 

172.  Traumatism  by  fall.     [For  example,  Accidental  fall  from  window.  ] 

173.  Traumatism  in  mines  and  quarries: 

Fall  of  rock  in  coal  mine, 

Injury  by  blasting,  slate  quarry,  etc. 

174.  Traumatism  by  machines.     [Specify  kind  of  machine,  and  if  the 

Occupation  is  not  fully  given  under  that  head,  add  sufficient  to 
show  the  exact  industrial  character  of  the  fatal  injury.  Thus, 
Crushed  by  passenger  elevator;  Struck  by  piece  of  emery 
wheel  (knife  grinder);  Elevator  accident  (pile  driver),  etc.] 


PRESENT  CLASSIFICATION  267 

175.  Traumatism  by  other  crushing: 

Railway  collision, 

Struck  by  street  car, 

Automobile  accident, 

Run  ove   by  dray, 

Crushed  by  earth  in  sewer  excavation,  etc. 

176.  Injuries  by  animals.     [Name  animal.] 

177.  Starvation.     [Not  "  inanition  "  from  disease.] 

178.  Excessive  cold.     [Freezing.] 

179.  Excessive  heat.     [Sunstroke.] 

180.  Lightning. 

181.  Electricity  (lightning  excepted).     [How?     Occupational?] 

182.  Homicide  by  firearms. 

183.  Homicide  by  cutting  or  piercing  instruments.     [Name  instru- 

ment.] 

184.  Homicide  by  other  means.     [Name  means.] 

185.  Fractures  (cause  not  specified).     [State  means  of  injury.    The 

nature  of  the  lesion  is  necessary  for  hospital  statistics  but 
not  for  general  mortality  statistics.] 

186.  Other  external  causes: 

Legal  hanging, 
Legal  electrocution, 

Accident,  injury,  or  traumatisml  (unqualified) .    [State  Means 
of  injury.] 


(XIV.  —  ILL-DEFINED  DISEASES) 

NOTE.  —  If  physicians  will  familiarize  themselves  with  the  nature 
and  purposes  of  the  International  List,  and  will  cooperate  with  the 
registration  authorities  in  giving  additional  information  so  that  returns 
can  be  properly  classified,  the  number  of  deaths  compiled  under  this 
group  will  rapidly  diminish,  and  the  statistics  will  be  more  creditable 
to  the  office  that  compiles  them  and  more  useful  to  the  medical  pro- 
fession and  for  sanitary  purposes. 

187.  Ill-defined  organic  disease: 

Dropsy,  Ascites}  etc.     [Name  the  disease  of  the  heart,  liver, 
or  kidneys  in  which  the  dropsy  occurred.] 

188.  Sudden  death.     [Give  cause.     Puerperal?] 


268  CAUSES  OF  DEATH 

189.  Cause  of  death  not  specified  or  ill-defined.  [It  may  be  extremely 
difficult  or  impossible  to  determine  definitely  the  cause  of  death 
in  some  cases,  even  if  a  post-mortem  be  granted.  If  the  physi- 
cian is  absolutely  unable  to  satisfy  himself  in  this  respect,  it  is 
better  for  him  to  write  Unknown  than  merely  to  guess  at  the 
cause.  It  will  be  helpful  if  he  can  specify  a  little  further,  as 
Unknown  disease  (which  excludes  external  causes),  or  Unknown 
chronic  disease  (which  excludes  the  acute  infective  diseases), 
etc.  Even  the  ill-defined  causes  included  under  this  head  are 
at  least  useful  to  a  limited  degree,  and  are  preferable  to  no 
attempt  at  statement.  Some  of  the  old  "chronics,"  which 
well-informed  physicians  are  coming  less  and  less  to  use,  are 
the  following:  Asphyxia;  Asthenia;  Bilious  fever;  Cachexia', 
Calarrhal  fever;  Collapse;  Coma;  Congestion;  Cyanosis;  De- 
bility;  Delirium;  Dentition;  Dyspnea;  Exhaustion;  Fever; 
Gastric  fever;  HEART  FAILURE;  Laparotomy;  Marasmus; 
Paralysis  of  the  heart;  Surgical  shock;  and  Teething.  In 
many  cases  so  reported  the  physician  could  state  the  disease 
(not  mere  symptom  or  condition)  causing  death.] 


PRESENT  CLASSIFICATION 


269 


LIST  OF  UNDESIRABLE  TERMS 


UNDESIRABLE  TERM. 
(It  is  understood  that  the  term 
criticised  is  in  the  exact  form 
given  below,  without  further  ex- 
planation or  qualification.) 


REASON  WHY  UNDESIRABLE,  AND  SUGGESTION  FOR 
MORE  DEFINITE  STATEMENT  OF  CAUSE  OF  DEATH. 


(1) 


Abscess,"   "  Abscett  of  brain," 
"  Abscess  of  lung,"  etc. 


Accident"  "  Injury"  "  External 
causes,"  "  Violence."  Also 
more  specific  terms,  as  "  Drown- 
ing," "  Gun-shot,"  which  might 
be  either  accidental,  suicidal, 
or  homicidal. 

Anasarca,"  "  Ascites." 

Atrophy,"  "  Asthenia,"  "  Debil- 
ity," "  Decline,"  "  Exhaustion," 
"  Inanition,"  "  Weakness,"  and 
other  vague  terms. 

Blood  poisoning  " 


1  Cancer,"  "  Carcinoma,"  "  Sar- 
coma," etc. 

'Catarrh" 

1  Cardiac  insufficiency,"  "  Cardiac 
degeneration,"  "  Cardiac  weak- 
ness," etc. 


Cardiac  dilatation 


Cellulitis" 

Cerebrospinal  meningitis." 

'  Congestion,"'1  Congestion  of  bow- 
els," "  Congestion  of  the  brain," 
"  Congestion  of  kidneys,"  "-Con- 
gestion of  lungs,"  etc. 


Was  it  tuberculous  or  due  to  other  infection?  Trau- 
matic? The  return  of  "  Abscess,"  unqualified,  is 
worthless.  State  cause  (in  which  case  the  fact  of 
"  abscess  "  may  be  quite  unimportant)  and  loca- 
tion. 

Impossible  to  classify  satisfactorily.  Always  state 
(1)  whether  Accidental,  Suicidal,*  or  Homicidal; 
and  (2)  Means  of  injury  (e.g.,  Railroad  accident). 
The  lesion  (e.g.,  Fracture  of  skull)  may  be  added, 
but  is  of  secondary  importance  for  general  mortal- 
ity statistics. 

See  "  Dropsy." 

Frequently  cover  tuberculosis  and  other  definite 
causes.  Name  the  disease  causing  the  condition. 


See  ' '  Septicemia.' '    Syphilis? 

In  all   cases    die  organ    or  part  first  affected  by 
cancer  should  be  specified. 

Term  best  avoided,  if  possible. 

See  "  Heart  disease  "  and  "  Heart  failure. 


Do  not  report  when  a  mere  terminal  condition. 
State  cause. 

See  "  Abscess,"  "  Septicemia" 
See  "  Meningitis." 

Alone,  the  word  "  congestion  "  is  worthless,  and  in 
combination  it  is  almost  equally  undesirable.  If 
the  disease  amounted  to  inflammation,  use  the 
proper  term  (lobar  pneumonia,  chronic  nephritis, 
enteritis,  etc.);  merely  passive  congestion  should 
not  be  reported  as  a  cause  of  death.  State  the 
primary  cause. 


270 


CAUSES  OF   DEATH 


LIST  OF  UNDESIRABLE  TERMS  (Continued) 


TKK  .1. 


REASON  WHY  UNDESIRABLE,  AND  SUGGESTION  FOB 
MORE  DEFINITE  STATEMENT  OF  CAUSE  OF  DKATH. 


(1) 


(2) 


Convulsions,"        "  Eclampsia," 
"  Fit,"  or  "  Fits." 


"  Croup  " . 


Dentition"  "  Teething  " 

Disease,"  "  Trouble,"  or  "  Com- 
plaint "  of  [any  organ\,  e.g., 
"  Lung  trouble,"  "  Kidney  com- 
plaint," "  Disease  of  brain,"  etc. 


Dropsy" . 


"  Edema  of  lungs  " . 
"Fever"... 


Fracture,"  "  Fracture  of  skull, 
etc. 


"  Gastritis,"     "  Gastric    catarrh, 
"  Acute  indigestion." 


'It  is  hoped  that  this  indefinite  term  ["  Convul- 
sions "]  will  henceforth  be  restricted  to  those  cases 
in  which  the  true  cause  of  that  symptom  can  not 
be  ascertained.  At  present  more  than  eleven  per 
cent  of  the  total  deaths  of  infants  under  one  year 
old  are  referred  to  '  convulsions  '  merely."  —  Reg- 
istrar-General. "  Fit.  —  This  is  an  objectionable 
term;  it  is  indiscriminately  applied  to  epilepsy, 
convulsions,  and  apoplexy  in  different  parts  of  the 
country."  —  Dr.  Fair,  in  First  Rep.  Reg.-Gen.,l$W. 

"  Croup  "  is  a  most  pernicious  term  from  a  public 
health  point  of  view,  is  not  contained  in  any  form 
in  the  London  or  Bellevue  Nomenclatures,  and 
should  be  entirely  disused.  Write  Diphtheria 
when  this  disease  is  the  cause  of  death. 

State  disease  causing  death. 

Name  the  disease,  e.g.,  Lobar  pneumonia,  Tuber- 
culosis of  lungs,  Chronic  interstitial  nephritis, 
Syphilitic  gumma  of  brain,  etc. 


'  '  Dropsy  '  should  never  be'returned  as  the  cause  of 
*  death  without  particulars  as  to  its  probable  origin, 
e.g.,  in  disease  of  the  heart,  liver,  kidneys,  etc."  — 
Registrar-General.  Name  the  disease  causing  (the 
dropsy  and)  death. 


Usually  terminal, 
condition. 


Name  the  disease  causing  the 


Name  the  disease,  as  Typhoid  fever,  Lobar  pneu- 
monia, Malaria,  etc.,  in  which  the  "  fever  " 

occurs. 

Indefinite;  the  principle  of  classification  for  general 
mortality  statistics  is  not  the  lesion  but  (1)  the 
nature  of  the  violence  that  produced  it  (Acciden- 
tal, Suicidal,  Homiddal),  and  (2)  the  Means  of 
injury. 

Frequently  worthless  as  a  statement  of  the  actual 
cause  of  death;  the  terms  should  not  be  loosely 
used  to  cover  almost  any  fatal  affection  with  irri- 
tation of  stomach.  Gastroenteritis?  Acute  or 
chronic,  and  cause? 


PRESENT  CLASSIFICATION 


271 


LIST  OF  UNDESIRABLE  TERMS  (Continued) 


UNDESIRABLE  TERM 


REASON  Wnr  UNDESIRABLE,  AND  SUGGESTION  TOR 
MORE  DEFINITE  STATEMENT  OF  OAFSE  OF  DEATH. 


(1) 


C2) 


General  decay,  etc. 


Heart  disease,"  "  Heart  trouble," 
even  "  Organic  heart  trouble." 


Heart  failure,"  "  Cardiac  weak- 
ness," "  Cardiac  asthenia,' 
"  Cardiac  exhaustion,"  "  Paraly- 
sis of  the  heart,  '  etc. 


Hemorrhage,"     "  Hemoptysis," 
"  Hemorrhage  of  lungs." 


Hydrocephalus 


Hysterectomy  " 


Infantile  asthenia,"  "  Infantile 
atrophy,"  "  Infantile  debility," 
"  Infantile  marasmus,"  etc. 


' Infantile  paralysis" . 


Inflammation". 
Laparotomy  " . . 


See  "Old  age." 

The  exact  form  of  the  cardiac  affection,  as  Mitral 
regurgitation,  Aortic  stenosis,  or,  less  precjsely, 
as  Valvular  heart  disease,  should  be  stated. 

"  Heart  failure  "  is  a  recognized  synonym,  even 
among  the  laity,  for  ignorance  of  the  cause  of  death 
on  the  part  of  the  physician.  Such  a  return  is  for- 
bidden by  law  in  Connecticut.  If  the  physician 
can  make  no  more  definite  statement,  it  must  be 
compiled  among  the  class  of  ill-defined  diseases 
(not  under  Organic  heart  disease). 

Frequently  mask  tuberculosis  or  deaths  from  in- 
juries (traumatic  hemorrhage),  Puerperal  hem- 
orrhage, or  hemorrhifee  after  operation  for  various 
conditions.  What  was  the  cause  and  location  of 
the  hemorrhage?  If  from  violence,  state  fully 
(p.  11). 

"It  is  desirable  that  deaths  from  hydrocephalus  of 
tuberculous  origin  should  be  definitely  assigned 
in  the  certificate  to  Tuberculous  meningitis,  so 
as  to  distinguish  them  from  deaths  caused  by 
simple  inflammation  or  other  disease  of  the  brain 
or  its  membranes.  Congenital  hydrocephalus 
should  always  be  returned  as  such."  —  Registrar- 
General. 

See  "  Operation.1' 

See  "Atrophy'." 


This  term  is  sometimes  used  for  paralysis  of  infants 
caused  by  i  strumental  delivery,  etc.  The  im- 
portance of  the  disease  in  its  recent  endemic  and 
epidemic  prevalence  in  the  United  States  makes 
the  exact  and  unmistakable  expressions  Acute  an- 
terior poliomyelitis  or  Infantile  paralysis  (acute 
anterior  poliomyelitis)  desirable. 

Of  what  organ  or  part  of  the  body?    Cause? 
See  "  Operation." 


272 


CAUSES  OF  DEATH 


LIST  OF  UNDESIRABLE  TERMS  (Continued) 


UNDESIRABLE  TERM. 


REASON  WHY  UNDESIRABLE,  AND  SUGGESTION  FOR 
MORE  DEFINITE  STATEMENT  OF  CAUSE  OF  DEATH. 


(D 


(2) 


Malignant,"     "  Malignant 
ease." 


dis- 


"  Malnutrition". 


1  Marasmus  " . 


Meningitis,"  "  Cerebral  meningi- 
tis,"  "  Cerebrospinal   meningi- 
tis," "  Spinal  meningitis." 


Natural  causes 


'Old  age,"  "  Senility,"  etc. 


Operation,"  "  Surgical  opera- 
tion," "  Surgical  shock,"  "  Am- 
putation," "  Hysterectomy," 
"  Laparotomy,"  etc. 


Should  be  restricted  to  use  as  qualification  for  neo- 
plasms; see  Tumor. 

See  "  Atrophy." 

This  term  covers  a  multitude  of  worthless  returns, 
many  of  which  could  be  made  definite  and  useful 
by  giving  the  name  of  the  disease  causing  the  "  ma- 
rasmus "  or  wasting.  It  has  been  dropped  from 
the  English  Nomenclature  since  1885  ("  Maras- 
mus, term  no  longer  used  ").  The  Bellevue  Hos- 
pital Nomenclature  also  omits  this  term. 

Only  two  terms  should  ever  be  used  to  report  deaths 
from  Cerebrospinal  fever,  synonym,  Epidemic 
cerebrospinal  meningitis,  and  they  should  be 
written  as  above  and  in  no  other  way.  It  matters 
not  in  tbe  use  of  the  latter  term  whether  the  disease 
be  actually  epidemic  or  not  in  the  locality.  A 
single  sporadic  case  should  be  so  reported.  The 
first  term  (Cerebrospinal  fever)  is  preferable  be- 
cause there  is  no  apparent  objection  to  its  use  for 
any  number  of  cases.  No  one  can  intelligently 
classify  such  returns  as  are  given  in  the  margin. 
Mere  terminal  or  symptomatic  meningitis  should 
not  be  entered  at  all  as  a  cause  of  death;  name  the 
disease  in  which  it  occurred.  Tuberculous  men- 
ingitis should  be  reported  as  such. 

This  statement  eliminates  external  causes,  but  is 
otherwise  of  little  value.  What  disease  (prob- 
ably) caused  death  ? 

Too  often  used  for  deaths  of  elderly  persons  who  suc- 
cumbed to  a  definite  disease.  Name  the  disease 
causing  death. 

All  these  are  entirely  indefinite  and  unsatisfactory 
—  unless  the  surgeon  desires  his  work  to  be  held 
primarily  responsible  for  the  death.  Name  the 
disease,  abnormal  condition,  or  form  of  ^external 
violence  (Means  of  death;  accidental,  suicidal, 
or  homicidal?),  for  which  the  operation  was  per- 
formed. If  death  was  due  to  an  anesthetic  (chlo- 
roform, ether,  etc.),  state  that  fact  and  the  name 
of  the  anesthetic. 


PRESENT  CLASSIFICATION 
LIST  OF  UNDESIRABLE  TERMS  (Continued) 


273 


UNDESIRABLE  TERM. 


REASON  WHY  UNDESIRABLE,  AND  SUGGESTION  FOR 
MORE  DEFINITE  STATEMENT  OF  CAUSE  OF  DEATH. 


(1) 


(2) 


Paralysis,"  "  General  paralysis," 
"  Paresis,"  "  General  paresis," 
"  Palsy,"  etc. 


Peritonitis ' 


Pneumonia,' 
monia." 


"  Typhoid    pneu- 


The  vague  use  of  these  terms  should  be  avoided,  and 
the  precise  form  stated,  as  Acute  ascending  paral- 
ysis, Paralysis  agitans,  Bulbar  paralysis,  etc. 
Write  General  paralysis  of  the  insane  in  full, 
not  omitting  any  part  of  the  name;  this  is  essential 
for  satisfactory  compilation  of  this  cause.  Distin- 
guish Paraplegia  and  Hemiplegia;  and  in  the 
latter,  when  a  sequel  of  Apoplexy  or  Cerebral 
hemorrhage,  report  the  primary  cause. 

"  Whenever  this  condition  occurs  —  either  as  a  con- 
sequence of  Hernia,  Perforating  ulcer  of  the 
stomach  or  bowel  [Typhoid  fever?],  Appendicitis, 
or]  Metritis  (puerperal  or  otherwise),  or  else 
as  an  extension  of  morbid  processes  from  other 
organs  [Name  the  disease],  the  fact  should  be 
mentioned  in  the  certificate."  —  Registrar-General. 
Always  specify  Puerperal  peritonitis  in  cases  re- 
sulting from  abortion,  miscarriage,  or  labor  at  full 
term.  Always  state  if  due  to  tuberculosis  or 
cancer.  When  traumatic,  report  means  of  injury 
and  whether  accidental,  suicidal,  or  homicidal. 

"  Pneumonia,"  without  qualification,  is  indefinite; 
it  should  be  clearly  stated  either  as  Bronchopneu- 
monia  or  Lobar  pneumonia.  The  term  Croup- 
ous  pneumonia  *is  also  clear.  "  The  term  '  Ty- 
phoid pneumonia  '  should  never  be  employed,  as  it 
may  mean  either  Enteric  fever  [Typhoid  fever] 
with  pulmonary  complications,  on  the  one  hand 
or  Pneumonia  with  so-called  typhoid  symptoms  on 
the  other."  —  Registrar-General.  When  lobar  pneu- 
monia or  bronchopneumonia  occurs  in  the  course 
of  or  following  a  disease  the  primary  cause  should 
be  entered  first,  with  duration,  and  the  lobar 
pneumonia  or  bronchopneumonia  be  entered  be- 
neath as  the  contributory  cause,  with  duration. 
Do  not  report  "  Hypostatic  pneumonia  "  or  other 
mere  terminal  conditions  as  causes  of  death  when 
the  disease  causing  death  can  be  ascertained. 


274 


CAUSES  OF  DEATH 


LIST  OF  UNDESIRABLE  TERMS  (Continued) 


UNDESIRABLE  TERM. 


REASON  WHY  UNDESIRABLE,  AND  SUGGESTION  FOB 
MORE  DEFINITE  STATEMENT  OF  CAUSE  OF  DEATH. 


(1) 


(2) 


Ptomain   poisoning,"    "  Autoin- 
toxication," "  Toxemia,"  etc. 


Pulmonary  congestion"   "  Pul- 
monary hemorrhage." 


Pyemia". 


Septicemia,"  "  Sepsis,"  "  Sep- 
tic infection,"  etc. 


'  Shock  "  (post-operative) 

'Specific" 


"  Tabes  mesenterica,"  "  Tabes  "... 


"  Teething" 

"  Toxemia" 

"Tuberculosis". 


'I  hese  terms  are  used  very  loosely  and  it  is  impos- 
sible to  compile  statistics  of  value  unless  greater 
precision  can  be  obtained.  They  should  not  be 
used  when  merely  descriptive  of  symptoms  or  con- 
ditions arising  in  the  course  of  diseases,  but  the 
disease  causing  death  should  alone  be  named. 
"  Ptomain  poisoning  "  should  be  restricted  to 
deaths  lesulting  from  the  development  of  putre- 
factive alkaloids  or  other  poisons  in  food,  and  the 
food  should  be  named,  as  Ptomain  poisoning 
(mussels),  etc. 

See  "  Congestion,"  "  Hemorrhage." 


See  "  Septicemia." 

Always  state  cause  of  this  condition,  and,  if  local- 
ized, pait  affected.  Puerperal?  Traumatic  (see 
p.  11)? 

See  "  Operation." 

The  word  specific  should  never  be  used  without 
further  explanation.  It  may  signify  syphilitic, 
tuberculous,  gonorrheal,  diphtheritic,  etc.  Name  the 
disease. 

"  The  use  of  this  term  ["  Tabes  mesenterica  "]  to  de- 
scribe tuberculous  disease  of  the  peritoneum  or  in- 
testines should  be  discontinued,  as  it  is  frequently 
used  to  denote  various  other  wasting  diseases 
which  are  not  tuberculous.  Tuberculous  perito- 
nitis is  the  better  term  to  employ  when  the  condi- 
tion is  due  to  tubercle."  —  Registrar-General. 
Tabes  dorsalis  should  not  be  abbreviated  to 
"  Tabes." 

See  "  Dentition." 

See  "  Ptomain  poisoning." 

The  organ  or  part  of  the  body  affected  should  always 
be  stated,  as  Tuberculosis  of  the  lungs,  Tuber- 
culosis of  the  spine,  Tuberculous  meningitis, 
Acute  general  miliary  tuberculosis,  etc. 


SYNONYMS  USED  FOR  "TYPHOID  FEVER"       275 


LIST  OF  UNDESIRABLE  TERMS  (Concluded) 


UNDESIRABLE  TERM. 


REASON  WHY  UNDESIRABLE,  AND  SUGGESTION  FOR 
MORE  DEFINITE  STATEMENT  OF  CAUSE  OF  DEATH. 


(1) 


C2) 


7\tmort"    "  Neoplasm,"    "  New 
growth" 


Uremia' 


Uterine  hemorrhage  " 


These  terms  should  never  be  used  without  the  qual- 
fying  words  Malignant,  Nonmalignant,  or  Be- 
nign. If  malignant,  they  belong  under  Cancer, 
and  should  preferably  be  so  reported,  or  under  the 
more  exact  terms  Carcinoma,  Sarcoma,  etc.  In 
all  cases  the  organ  or  pait  affected  should  be 
specified. 

Name  the  disease  causing  death,  i.e.,  the  primary 
cause,  not  the  mere  terminal  conditions  or  symp- 
toms, and  state  the  duration  of  the  primary 


See  "  Hemorrhage." 


Some  of  the  synonyms  used  for  "  typhoid  fever."  —  The 

following  is  a  partial  list  of  terms  which  have  been  used  to 
describe  typhoid  fever: 


Abdominal  fever, 
Abdominal  typhoid, 
Abdominal  typhus, 
Abortive  typhoid, 
Ambulant  typhoid, 
Cerebral  typhoid, 
Cerebral  typhus 
Continued  fever, 
Enteric  fever, 
Enterica, 

Gastroenteric  fever 
H*morrhagic  typhoid  fever, 
Ileotyphus, 

Intermittent  typhoid  fever, 
Malignant  typhoid  fever, 
Mountain  fever, 
Paratyphoid  fever. 

This  shows  the  great  need  of  standardization. 


Paratyphus, 
Posttyphoid  abscess 
Rheumatic  typhoid  fever, 
Typhpbilious  fever, 
Typhoenteritis, 
Typhogastric  fever, 
Typhoid  fever, 
Typhoid  malaria, 
Typhoid  meningitis, 
Typhoid  stupor, 
Typhoid  ulcer 
Typhomalaria, 
Typhornalarial  feve,r, 
Typhoperitonitis, 
Typhus 
Typhus  abdommalis. 


276  CAUSES  OF  DEATH 

Joint  causes  of  death.  —  The  Bureau  of  the  Census  in 
1914  published  an  "  Index  of  Joint  Causes  of  Death,"  which 
shows  the  proper  method  of  assignment  to  the  preferred 
title  of  causes  of  death  when  two  causes  are  simultaneously 
reported.  This  index,  alphabetically  arranged,  is  very 
useful.  Physicians  sometimes  report  two  or  more  causes 
of  death  upon  the  death-certificate.  This  may  be  histori- 
cally true  as  one  disease  may  be  a  complication  of  the  other. 
For  statistical  purposes,  however,  only  one  cause  can  be 
tabulated  for  each  death.  Out  of  the  two  or  more  causes 
given  one  must  be  selected,  and  it  is  a  matter  of  great  impor- 
tance how  this  is  done.  For  some  years  the  attempt  has 
been  made  to  separate  the  diseases  reported  into  the  primary 
cause  and  secondary  cause.  As  this  gave  rise  to  some  uncer- 
tainty as  to  which  was  which,  the  form  of  the  Revised  U.  S. 
Standard  Certificate  of  Death  asks  for  "  The  Cause  of  Death  " 
and  for  "The  Contributory  Cause  (Secondary)."  The  Eng- 
lish, French  and  Germans  have  laid  down  certain  rules  for 
making  the  proper  selections.  In  general,  it  may  be  said  that 
the  primary  cause  is  the  real,  or  underlying,  cause  of  death 
(the  primary  affection  with  respect  to  time  and  causation). 
The  following  are  the  American  instructions  as  printed  on 
the  back  of  the  standard  death-certificate. 


STANDARD   CERTIFICATE  OF  DEATH 

Statement  of  occupation.  —  Precise  statement  of  occupation  is  very 
important,  so  that  the  relative  healthfulness  of  various  pursuits  can  be 
known.  The  question  applies  to  each  and  every  person,  irrespective  of 
age.  For  many  occupations  a  single  word  or  term  on  the  first  line  will 
be  sufficient,  e.g.,  Farmer  or  Planter,  Physician,  Compositor,  Architect, 
Locomotive  engineer,  Civil  engineer,  stationary  fireman,  etc.  But  in 
many  cases,  especially  in  industrial  employments,  it  is  necessary  to 
know  (a)  the  kind  of  work  and  also  (6)  the  nature  of  the  business  or 
industry,  and  therefore  an  additional  line  is  orovided  for  the  latter 
statement;  it  should  be  used  only  when  needed.  As  examples:  (a) 


JOINT  CAUSES  OF  DEATH  277 

Spinner,  (6)  Cotton  mill,  (a)  Salesman,  (b)  Grocery,  (a)  Foreman,  (b) 
Automobile  factory.  The  material  worked  on  may  form  part  of  the 
second  statement.  Never  return  "  Laborer,"  "  Foreman,"  "  Manager," 
"  Dealer,"  etc.,  without  more  precise  specification,  as  Day  laborer,  Farm 
laborer,  Laborer  —  Coal  mine,  etc.  Women  at  home  who  are  engaged 
in  the  duties  of  the  household  only  (not  paid  Housekeepers  who  receive 
a  definite  salary)  may  be  entered  as  Housewife,  Housework,  or  At 
home,  and  children,  not  gainfully  employed,  as  At  school  or  At  home. 
Care  should  be  taken  to  report  specifically  the  occupations  of  persons 
engaged  in  domestic  service  for  wages,  as  Servant,  Cook,  Housemaid, 
etc.  If  the  occupation  has  been  changed  or  given  up  on  account  of 
the  DISEASE  CAUSING  DEATH,  state  occupation  at  beginning  of  illness. 
If  retired  from  business,  that  fact  may  be  indicated  thus:  Farmer 
(retired,  6  yrs.).  For  persons  who  have  no  occupation  whatever,  write 
None. 

Statement  of  cause  of  death.  —  Name,  first,  the  DISEASE  CAUSING 
DEATH  (the  primary  affection  with  respect  to  time  and  causation), 
using  always  the  same  accepted  term  for  the  same  disease.  Examples: 
Cerebro-spinal  fever  (the  only  definite  synonym  is  "  Epidemic  cerebro- 
spinal  meningitis");  Diphtheria  (avoid  use  of  "Croup");  Typhoid 
fever  (never  report  "  Typhoid  pneumonia  ");  Lobar  pneumonia ;  Bron- 
chopneumonia  ("  Pneumonia,"  unqualified,  is  indefinite);  Tuber- 
culosis of  lungs,  meninges,  peritoneum,  etc.,  Carcinoma,  Sarcoma,  etc., 

of (name  origin:  "  Cancer  "  is  less  definite;  avoid  use  of 

^Tumor"  for  malignant  neoplasms);  Measles;  Whooping  cough; 
Chronic  valvular  heart  disease;  Chronic  interstitial  nephritis,  etc.  The 
contributory  (secondary  or  intercurrent)  affection  need  not  be  stated 
unless  important.  Example:  Measles  (disease  causing  death),  29  ds.; 
Broncho-pneumonia  (secondary),  10  ds.  Never  report  mere  symptoms 
or  terminal  conditions,  such  as  "  Asthenia,"  "  Anemia,"  (merely 
symptomatic),  "  Atrophy,"  "  Collapse,"  "  Coma,"  "  Convulsions," 
"Debility"  ("Congenital,"  "Senile,"  etc.),  "Dropsy,"  "Exhaus- 
tion," "  Heart  failure,"  "  Hemorrhage/'  "  Inanition,"  "  Marasmus," 
"  Old  age,"  "  Shock,"  "  Uremia,"  "  Weakness,"  etc.,  when  a  definite 
disease  can  be  ascertained  as  the  cause.  Always  qualify  all  diseases 
resulting  from  childbirth  or  miscarriage,  as  "  Puerperal  septicemia," 
"  Puerperal  peritonitis,"  etc.  State  cause  for  which  surgical  operation 
was  undertaken. 

For  VIOLENT  DEATHS  state  MEANS  OF  INJURY  and  qualify  as  ACCI- 
DENTAL, SUICIDAL,  or  HOMICIDAL,  or  as  probably  such,  if  impossible  to 
determine  definitely.  Examples :  Accidental  drowning;  Struck  by  railway 


278  CAUSES  OF  DEATH 

train  —  accident;  Revolver  wound  of  head  —  homicide;  Poisoned  by  carbolic 
acid  —  probably  suicide.  The  nature  of  the  injury,  as  fracture  of  skull, 
and  consequences  (e.  g.,  sepsis  tetanus}  may  be  stated  under  the  head  of 
"  Contributory."  (Recommendations  on  statement  of  cause  of  death 
approved  by  Committee  on  Nomenclature  of  the  American  Medical 
Association.) 

Cases  for  the  Medical  Examiners.  —  Under  the  provisions  of  chapter 
24  of  the  Revised  Laws  deaths  under  the  following  conditions  must  be 
referred  to  the  Medical  Examiners: 

1.  Deaths  following  injury  or  violence,  as  Burns,  Falls,  Drowning, 

Gas  poisoning,  Suicide,  Homicide,  etc. 

2.  Deaths  supposedly   caused   by   violence,   as   Criminal  abortion, 

Poisoning,  Starvation,  Suffocation,  Exposure,  etc. 

3.  Sudden  deaths  of  persons  not  disabled  by  recognized  disease,  as 

A  death  upon  the  street,  or  one  supposed  to  be  due  to  Alcoholism,  etc. 

4.  Deaths  under  circumstances  unknown,  as  A  person  found  dead,  etc. 

The  following  supplementary  suggestions  are  also  useful.1 
J- 1.   Select  the  primary  cause,  that  is,  the  real  or  under- 
lying cause  of  death.     This  is  usually  — 
(a)  The  cause  first  in  order. 

(6)  The  cause  of  longer  duration.  If  the  physician 
writes  the  cause  of  shorter  duration  first,  in- 
quiry may  be  made  whether  it  is  not  a  mere 
symptom,  complication,  or  terminal  condition. 

(c)  The  cause  of  which  the  contributory  (secondary) 

cause  is  a  frequent  complication.  See  lists  of 
"  Frequent  complications  "  under  the  various 
titles  of  the  Tabular  List. 

(d)  The  physician  may  indicate  the  relation  of  the 

causes  by  words,  although  this  is  a  departure 
from  the  way  in  which  the  blank  was  in- 
tended to  be  filled  out.  For  example, 
"  Bronchopneumonia  following  measles'" 
(primary  cause  last)  or  "  measles  followed  by 
brochopneumonia  "  (primary  cause  first). 

1  Manual,  1911,  1,  p.  23. 


JOINT  CAUSES  OF   DEATH  279 

2.  If  the  relation  of  primary  and  secondary  is  not  clear, 
prefer  general  diseases,  and  especially  dangerous  infective 
or  epidemic  diseases,  to  local  diseases. 

3.  Prefer  severe  or  usually  fatal  diseases  to  mild  dis- 
eases. 

4.  Disregard    ill-defined  causes  (Class  XIV),  and  also 
indefinite  and   ill-defined  terms  (e.g.,  "  debility,"  "  atro- 
phy ")  in  Classes  XI  and  XII  that  are  referred,  for  certain 
ages,   to  Class  XIV,   as  compared  with  definite   causes. 
Neglect  mere  modes  of  death  (failure  of  heart  or  respira- 
tion) and  terminal  symptoms  or  conditions  (e.g.,  hypostatic 
congestion  of  lungs). 

5.  Select  homicide  and  suicide  in  preference  to  any  con- 
sequences,   and    severe    accidental    injuries,    sufficient    in 
themselves  to  cause  death,  to  all  ordinary  consequences. 
Tetanus  is  preferred   to  any  accidental   injury  and  ery- 
sipelas,   septicaemia,    pyaemia,    peritonitis,    etc.,    are    pre- 
ferred to  less  serious  accidental  injuries.     Prefer  definite 
means  of  accidental  injury  (e.g.,  railway  accident,  explosion 
in  coal  mine,  etc.)  to  vague  statements  or  statement  of  the 
nature  of  the  injury  only  (e.g.,  accident,  fracture  of  skull). 

6.  Physical  diseases  (e.g.,  tuberculosis  of  lungs,  diabetes) 
are  preferred  to  mental  diseases  as  causes  of  death  (e.g., 
manic  depressive  psychosis),  but  general  paralysis  of  the 
insane  is  a  preferred  term. 

7.  Prefer  puerperal  causes  except  when  a  serious  dis- 
ease (e.g.,  cancer,  chronic  Bright's  disease)  ^was  the  inde- 
pendent cause. 

8.  Disregard  indefinite   terms   and   titles    generally  in 
favor  of  definite  terms  and  titles.     The  precise  line  of 
demarcation  is  difficult  to  lay  down,  but  may  be  indicated 
broadly  by  the  kinds  of  type  employed  in  the  International 
List  presented  on  page  35.     The  List  in  this  form  has  been 
distributed  by  the  Census  to  all  physicians  in  the  United 


280  CAUSES  OF  DEATH 

States,1  so  that  the  proportion  of  indefinite  returns  should 
become  less. 

Occupation.  —  During  recent  years  the  study  tf  the  rela- 
tion between  occupation  and  disease  has  received  much 
attention,  and  this  study  has  shown  the  very  great  impor- 
tance of  the  industrial  hazard.  Fundamental  to  such  a 
study  is  a  proper  classification  of  occupations.  The  list 
which  follows  was  published  by  the  Bureau  of  the  Census  in 
1915.  It  is  taken  from  a  report  entitled  "  Index  to  Occupa- 
tions, alphabetical  and  classified,"  a  book  of  414  pages. 

This  classification  contains  215  main  groups,  84  of  which 
are  subdivided,  making  a  total  of  428  separate  groups.  The 
industrial  field  is  divided  into  eight  general  divisions,  and 
each  occupation  has  been  "  classified  in  that  part  of  the 
industrial  field  in  which  it  is  most  commonly  pursued." 
Clerical  occupations  are  classified  apart.  The  classification 
'is  along  occupational  rather  than  industrial  lines.  In  the 
table  each  occupation  is  indicated  by  a  symbol  consisting  of 
three  figures,  the  first  of  which  indicates  one  of  the  following 
main  divisions: 

0.  Agriculture,  forestry  and  animal  husbandry. 

1.  Extraction  of  minerals. 

2.1 


3. 


Manufacturing  and  mechanical  industries. 


4. 

5.  Transportation. 

6.  Trade. 

1  Public  Service. 

*J  Professional  Service. 

8.  Domestic  and  Personal  Service. 

9.  Clerical  Occupations. 

1  See  Physicians'  Pocket   Reference  to   the  International  List  of 
Causes  of  Death. 


OCCUPATIONS  281 

The  second  and  third  figures  of  each  symbol  are  used  in 
combination  and  indicate  the  occupation  under  the  given 
main  division.  Thus  in  the  symbol  529,  5  stands  for  "  Trans- 
portation" and  29  for  "  Brakeman-steam  railroad." 

The  report  emphasizes  the  need  of  great  care  in  distinguish- 
ing between  occupations  and  gives  the  following  as  examples 
of  distinctions  which  must  be  made :  — 

An  iron  foundry  and  a  brass  foundry. 

A  felt  hat  factory  and  a  straw  hat  factory. 

A  steam  railroad  and  a  street  railway. 

A  paper  box  and  a  wooden  box  factory. 

A  locomotive  engineer  and  a  stationary  engineer. 

A  wholesale  and  a  retail  merchant  or  dealer. 

A  clerk  in  a  store  and  a  salesman. 

A  machinist  and  a  machine  tender. 

A  paid  housekeeper  and  a  housewife  in  her  own  home. 

A  paid  housekeeper  and  a  servant  girl. 

A  cook  and  a  servant. 

A  proprietor  and  an  employee,  etc. 

LIST  OF  OCCUPATIONS  AND   OCCUPATION  GROUPS  WITH 
THEIR  SYMBOLS 

Symbol.  Occupation  and  occupation  group. 

Agriculture,   Forestry,  and  Animal  Husbandry 

0  1  0 ....     Dairy  farmers 

0  1  2 ....     Dairy  farm  laborers 

0  1  4 Farmers1 

Farm  laborers 

0  2  1 Farm  laborers  (home  farm) 

0  2  2.  ...         Farm  laborers  (working  out) 
0  2  3 ....        Turpentine  farm  laborers 

Farm,  dairy  farm,  garden,  orchard,  etc.,  foremen 
0  2  5 ....         Dairy  farm  foremen 

0  26 Farm  foremen2 

0  2  7 ....         Garden  and  greenhouse  foremen 
0  2  8. ...         Orchard,  nursery,  etc.,  foremen 

1  Includes  turpentine  farmers.  2  Includes  turpentine  farm  foremen. 


282  CAUSES  OF   DEATH 

Symbol  Occupation  and  occupation  group. 

Agriculture.  Forestry,  and  Animal  Husbandry  —  Continued 

0  3  3 ....     Fishermen  and  oystermen 
0  3  5 Foresters 

Gardeners,  florists,  fruit  growers,  and  nurserymen 

0  4  2 Florists 

0  4  3 ....         Fruit  growers  and  nurserymen 

0  4  4.  ...         Gardeners 

0  4  5 ....         Landscape  gardeners 

Garden,  greenhouse,  orchard,  and  nursery  laborers 
05     ....         Cranberry  bog  laborers 
0  5  5 ....         Garden  laborers 
0  5  6. ...         Greenhouse  laborers 
0  5  7 ....         Orchard  and  nursery  laborers 

Lumbermen,  raftsmen,  and  woodchoppers 
0  6  5 ....         Foremen  and  overseers 
0  6  6. ...         Lumbermen  and  raftsmen 
0  6  7 ....         Teamsters  and  haulers 
0  6  8. ...         Woodchoppers  and  tie  cutters 

0  7  5. ...     Owners  and  managers  of  log  and  timber  camps 
0  7  7 ....     Stock  herders,  drovers,  and  feeders 
0  7  9 Stock  raisers 

Other  agricultural  and  animal  husbandry  pursuits 
0  8  5 ....        Apiarists 
0  8  6 ....        Corn  shellers,  hay  balers,  grain  threshers,  etc. 

0  8  7 Ditchers  (farm) 

0  8  8.  ...         Poultry  raisers  and  poultry  yard  laborers 

0  8  9 Other  and  not  specified  pursuits 

Extraction  of  Minerals 

Foremen,  overseers,  and  inspectors 

1  0  0 ....         Foremen  and  overseers 
1  0  1 ....         Inspectors 

Operators,  officials,  and  managers 
1  1  0 ....         Managers 

1  1  1 Officials 

1  1  2 Operators 


OCCUPATIONS  283 

Symbol.  Oceuoation  and  occupation  group. 

Extraction  of  Minerals  —  Continued 

1  2  2 ....  Coal  mine  operatives 

1  3  3 ....  Copper  mine  operatives 

1  4  4. ...  Gold  and  silver  mine  operatives 

1  5  5 ....  Iron  mine  operatives 

Operatives  in  other  and  not  specified  mines 

1  6  6 Lead  and  zinc  mine  operatives 

167 All  other  mine  operatives 

1  7  7 ....     Quarry  operatives 

Oil,  gas,  and  salt  well  operatives 
1  8  8 Oil  and  gas  well  operatives 

1  8  9 Salt  well  and  works  operatives 

Manufacturing  and  Mechanical  Industries 
Apprentices 

2  0  0 Apprentices  to  building  and  hand  trades 

2  0  1 Dressmakers'  and  milliners'  apprentices 

2  0  2 Other  apprentices 

210 Bakers 

Blacksmiths,  forgemen,  and  hammermen 

2  1  1 Blacksmiths 

2  1  2 Forgemen,  hammermen,  and  welders 

2  1  3 ....  Boiler  makers 

2  1  4 ....  Brick  and  stone  masons 

2  1  5 ....  Builders  and  building  contractors 

2  1  6 ....  Butchers  and  dressers  (slaughterhouse) 

2  1  7 ....  Cabinetmakers 

2  1  8.  ...  Carpenters 

2  1  9 ....  Compositors,  linotypers,  and  typesetters 

2  "2  0 Coopers 

2  2  1 ....  Dressmakers  and  seamstresses  (not  in  factory) 

2  22 Dyers 

2  2  3 Electricians  and  electrical  engineers 

Electrotypers,  stereotypers,  and  lithographers 

2  2  4 Electrotypers  and  stereotypers 

2  2  5 Lithographers 


284  CAUSES  OF  DEATH 

Symbol.  Occupation  and  occupation  group. 

Manufacturing  and  Mechanical  Industries  —  Continued 

2  2  6 ....     Engineers  (mechanical) 
2  2  7 ....     Engineers  (stationary) 
228 Engravers 

Filers,  grinders,  buffers,  and  polishers  (metal) 

2  3  0 Buffers  and  polishers 

231 Filers 

2  3  2 Grinders 

2  3  3 ....     Firemen  (except  locomotive  and  fire  department) 
2  3  4 ....     Foremen  and  overseers  (manufacturing) 

Furnace  men,  smelter  men,  heaters,  pourers.  etc. 
2  3  5 ....         Furnace  men  and  smelter  men 

236 Heaters 

2  3  7 ....         Ladlers  and  pourers 
238 Puddlers 

2  3  9 Glass  blowers 

Jewelers,  watchmakers,  goldsmiths,  and  silversmiths 
2  4  0 ....         Goldsmiths  and  silversmiths 
2  4  1 ....         Jeweler.-;  and  lapidaries  (factory) 
2  4  2. ...         Jewelers  and  watchmakers  (not  in  factory) 

Laborers  (n.  o.  s.1) 

Building  and  hand  trades 

2  4  3 ....  General  and  not  specified  laborers 

244 Helpers  in  building  and  hand  trades 

Chemical  industries 
2  4  5. ...  Fertilizer  factories 

2  4  6 Paint  factories 

2  4  7 Powder,  cartridge,  fireworks,  etc.,  factories 

2  4  8. ...  Other  chemical  factories 

Clay,  glass,  and  stone  industries 
2  5  0 ....  Brick,  tile,  and  terra-cotta  factories 

2  5  1 ....  Glass  factories 

2  5  2 Lime,  cement,  and  gypsum  factories 

2  5  3 ....  Marble  and  stone  yards 

254  Potteries 

1  Not  otherwise  specified. 


OCCUPATIONS  285 

Symbol.  Occupation  and  occupation  group. 

Manufacturing  and  Mechanical  Industries  —  Continued 

Iron  and  steel  industries 
2  5  5 ....  Automobile  factories 

2  5  6. ...  Blast  furnaces  and  rolling  mills1 

2  5  7 ....  Car  and  railroad  shops 

2  5  8. ...  Wagon  and  carriage  factories 

2  5  9 ....  Other  iron  and  steel  works 

Other  metal  industries 

263 Brass  mills 

2  6  4. ...  Copper  factories 

2  6  5 ....  Lead  and  zinc  factories 

2  6  6. ...  Tinware  and  enamelware  factories 

2  6  7 Other  metal  factories 

Lumber  and  furniture  industries 
2  7  0. ...  Furniture,  piano,  and  organ  factories 

2  7  1 ....  Saw  and  planing  mills 2 

272 Other  woodworking  factories 

Textile  industries 

275 Cotton  mills 

2  7  6. ...  Silk  mills 

2  7  7 ....  Woolen  and  worsted  mills 

2  7  8 Other  textile  mills 

Other  industries 

2  8  0 Charcoal  and  coke  works 

2  8  1 ....  Cigar  and  tobacco  factories 

2  8  2 Clothing  industries 

2  8  3 ....  Electric  light  and  power  plants 

2  8  4. ...  Electrical  supply  factories 
Food  industries  — 

290 Bakeries 

2  9  1 ....  Butter  and  cheese  factories 

2  9  2 ....  Fish  curing  and  packing 

2  9  3 ....  Flour  and  grain  mills 

2  9  4 ....  Fruit  and  vegetable  canning,  etc. 

2  9  5 ....  Slaughter  and  packing  houses 

2  9  6 ....  Sugar  factories  and  refineries 

2  9  7 Other  food  factories 

1  Includes  tinpiate  mills.  2  Includes  wooden  box  factories. 


286  CAUSES  OF  DEATH 

Symbol.  Occupation  and  occupation  group. 

Manufacturing  and  Mechanical  Industries  —  Continued 

300 Gas  works 

3  0  1 ....  Liquor  and  beverage  industries 

3  0  2 Oil  refineries 

3  0  3 Paper  and  pulp  mills 

3  0  4 Printing  and  publishing 

3  0  5 Rubber  factories 

3  0  6 Shoe  factories 

3  0  7 Tanneries 

3  0  8. ...  Turpentine  distilleries 

3  0  9 Other  factories 

3  1  0 Loom  fixers 

Machinists,  millwrights,  and  toolmakers 
3  1  1 ....         Machinists  and  millwrights 
3  "1  2 ....         Toolmakers  and  die  setters  and  sinkers 

3  1  3 ....     Managers  and  superintendents  (manufacturing) 

Manufacturers  and  officials 
3  1  4 ....         Manufacturers 
3  1  5 Officials 

Mechanics  (n.  o.  s.1) 
3  1  6 ....         Gunsmiths,  locksmiths,  and  bellhangers 

3  1  7 Wheelwrights 

3  1  8. ...         Other  mechanics 

320 Millers  (grain,  flour,  feed,  etc.) 

3  2  1 ....     Milliners  and  millinery  dealers 

Molders,  founders,  and  casters  (metal) 
32  2. ...         Brass  molders,  founders,  and  casters 
3  2  3 ....         Iron  molders,  founders,  and  casters 
3  2  4. ...         Other  molders,  founders,  and  casters 

3  2  6 ....     Oilers  of  machinery 

Painters,  glaziers,  varnishers,  enamelers,  etc. 
3  2  7.  ...         Enamelers,  lacquerers,  and  japanners 
3  2  8.  ...         Painters,  glaziers,  and  varnishers  (building) 
3  2  9. ...         Painters,  glaziers,  and  varnishers  (factory) 

1  Not  otherwise  specified. 


OCCUPATIONS  287 

Symbol.  Occupation  and  occupation  group. 

Manufacturing  and  Mechanical  Industries  —  (Continued) 

3  3  0 Paper  hangers 

3  3  1 ....  Pattern  and  model  makers 

3  3  2 Plasterers 

3  3  3 ....  Plumbers  and  gas  and  steam  fitters 

3  3  4 ....  Pressmen  (printing) 

3  3  5.  ...  Rollers  and  roll  hands  (metal) 

3  3  6 Roofers  and  slaters 

3  3  7 Sawyers 

Semiskilled  operatives  (n.  o.  s.1) 
Chemical  industries 

340 Paint  factories 

3  '4  1 ....  Powder,  cartridge,  fireworks,  etc.,  factories 

3  4  2. ...  Other  chemical  factories 

3  4  4 Cigar  and  tobacco  factories 

Clay,  glass,  and  stone  industries 
3  4  5. ...  Brick,  tile,  and  terra-cotta  factories 

3  4  6. ...  Glass  factories 

3  4  7 ....  Lime,  cement,  and  gypsum  factories 

3  4  8. ...  Marble  and  stone  yards 

3  4  9 Potteries 

Clothing  industries 

3  5  5 Hat  factories  (felt) 

3  5  6. ...  Suit,  coat,  cloak,  and  overall  factories 

3  5  7 ....  Other  clothing  factories 

Food  industries 

360 Bakeries 

3  6  1 ...  Butter  and  cheese  factories 

3  6  2 Candy  factories 

3  6  3 ....  Flour  and  grain  mills 

3  6  4. ...  Fruit  and  vegetable  canning,  etc. 

3  6  5 ....  Slaughter  and  packing  houses 

3  6  & Other  food  factories 

3  6  9 ....         Harness  and  saddle  industries 

1  Not  otherwise  specified. 


288  CAUSES  OF  DEATH 

Symbol.  Occupation  and  occupation  group. 

Manufacturing  and  Mechanical  Industries  —  (Continued) 

Iron  and  steel  industries 
3  7  0 ....  Automobile  factories 

3  7  1 Blast  furnaces  and  rolling  mills l 

3  7  2 ....  Car  and  railroad  shops 2 

3  7  3 ....  Wagon  and  carriage  factories 

3  7  4. ...  Other  iron  and  steel  works 

Other  metal  industries 

380 Brass  mills 

3  8  1 ....  Clock  and  watch  factories 

3  8  2 Gold  and  silver  and  jewelry  factories 

3  8  3. .'. .  Lead  and  zinc  factories 

3  8  4 Tinware  and  enamelware  factories 

3  8  5 Other  metal  factories 

Liquor  and  beverage  industries 

3  9  0 Breweries 

3  9  1 Distilleries 

3  9  2 Other  liquor  and  beverage  factories 

Lumber  and  furniture  industries 

3  9  4. ...  Furniture,  piano,  and  organ  factories 

3  9  5 Saw  and  planing  mills 3 

3  9  6. ...  Other  woodworking  factories 

4  0  0. ...         Paper  and  pulp  mills 
40  1 ....         Printing  and  publishing 
402 Shoe  factories 

4  0  3 Tanneries 

Textile  industries  — 

Beamers,  warpers,  and  slashers 

4  0  5 Cotton  mills 

406....  Silk  mills 

4  0  7 ....  Woolen  and  worsted  mills 

40  8 Other  textile  mills 

Bobbin  boys,  doffers,  and  carriers 

4  1  0 Cotton  mills 

4  1  1 ....  Silk  mills 

4  1  2 ....  Woolen  and  worsted  mills 

4  1  3 Other  textile  mills 

1  Includes  tinplate  mills.  2  Includes  car  repairers  for  street  and  steam  railroads. 

3  Includes  wooden  box  factories. 


OCCUPATIONS  289 

Symbol.  Occupation  and  occupation  group. 

Manufacturing  and  Mechanical  Industries  —  (Continued) 

Carders,  combers,  and  lappers 

4  1  5 Cotton  mills 

4  i  6 Silk  mills 

4  i  7 ....  Woolen  and  worsted  mills 

4  1  8 Other  textile  mills 

Drawers,  rovers,  and  twisters 
4  2  0 ....  Cotton  mills 

4  2  1 Silk  mills 

4  2  2 ....  Woolen  and  worsted  mills  • 

4  2  3 Other  textile  mills 

Spinners 

425 Cotton  mills 

426 Silk  mills 

4  2  7 ....  Woolen  and  worsted  mills 

428 Other  textile  mills 

Weavers 

4  3  0 Cotton  mills 

4  3  1 Silk  mills 

4  3  2 ....  Woolen  and  worsted  mills 

4  3  3 ....  Other  textile  mills 

Winders,  reelers,  and  spoolers 
4  3  5....  Cotton  mills 

4  3  6! . . .  Silk  mills 

4  3  7. ...  Woolen  and  worsted  mills 

4  3  8. ...  Other  textile  mills 

Other  occupations 

440 Cotton  mills 

441....  Silk  mills 

4  4  2 ....  Woolen  and  worsted  mills 

4  4  3 Other  textile  mills 

Other  industries 

4  6  0 ....  Electrical  supply  factories 

4  6  1 ....  Paper  box  factories 

4  6  2 Rubber  factories 

4  6  3 ....  Other  factories 


290  CAUSES  OF  DEATH 

Symbol.  Occupation  and  occupation  group. 

Manufacturing  and  Mechanical  Industries  —  (Continued) 
4  7  0 ....     Sewers  and  sewing  machine  operators  (factory)  * 
4  7  1 ....     Shoemakers  and  cobblers  (not  in  factory) 

Skilled  occupations  (n.  o.  s.2) 
4  7  2. ...         Annealers  and  temperers  (metal) 
4  7  3 ....         Piano  and  organ  tuners 
4  7  4. ...         Wood  carvers 
4  7  5 ....         Other  skilled  occupations 
4  8  0.  ...     Stonecutters 
4  8  1 ....     Structural  iron  workers  (building) 
4  8  2. ...     Tailors  and'tailoresses 

Tinsmiths  and  coppersmiths 
4  8  3 ....         Coppersmiths 
4  8  4 Tinsmiths 

4  8  5. ...     Upholsterers 

Transportation 
Water  transportation  (selected  occupations) 

5  0  0. ...         Boatmen,  canal  men,  and  lock  keepers 
502  ...         Captains,  masters,  mates,  and  pilots 

5  0  4. ...         Longshoremen  and  stevedores 
5  0  6. ...         Sailors  and  deck  hands 

Road  and  street  transportation  (selected  occupations) 
5  0  8. ...         Carriage  and  hack  drivers 

5  1  0 Chauffeurs 

5  1  2. ...         Draymen,  teamsters,  and  expressmen3 

5  1  4. ...         Foremen  of  livery  and  transfer  companies 

5  1  6. ...         Garage  keepers  and  managers 

5  1  8.  ...         Hostlers  and  stable  hands 

5  2  0 ....         Livery  stable  keepers  and  managers 

5  2  2 ....         Proprietors  and  managers  of  transfer  companies 

Railroad  transportation  (selected  occupations) 

Baggagemen  and  freight  agents 
5  2  4. ...  Baggagemen 

5  2  5.  ...  Freight  agents 

1  Includes  sewers  and  sewing  machine  operators  in  all  factories  except  shoe  and  harness 
factories,  and  sack  sewers  in  fertilizer,  salt,  and  sugar  factories,  and  cement,  flour,  and 
grain  mills. 

2  Not  otherwise  specified. 

3  Teamsters  in  agriculture,  forestry,  and  the  extraction  of  minerals  are  classified  with 
the  other  workers  in  those  industries,  respectively;  and  drivers  for  bakeries  and  laundries 
are  classified  with  deliverymen  in  trade. 


OCCUPATIONS  291 

Symbol.  Occupation  and  occupation  group. 

Transportation  —  (Continued) 

5  2  7. ...  Boiler  washers  and  engine  hostlers 

529 Brakemen 

5  3  0 ....  Conductors  (steam  railroad) 

5  3  2 ....  Conductors  (street  railroad) 

5  3  4 ....  Foremen  and  overseers 
Laborers 

5  3  6 Steam  railroad  *>H 

5  3  7 Street  railroad 

5  3  9 ....  Locomotive  engineers 

H  4  0 ....  Locomotive  firemen 

5  4  2 ....  Motormen 

Officials  and  superintendents    . 
5  4  4. ...  Steam  railroad 

5  4  5 ....  Street  railroad 

Switchmen,  flagmen,  and  yardmen 

5  4  7 ....  Switchmen  and  flagmen  (steam  railroad) 

5  4  8. ...  Switchmen  and  flagmen  (street  railroad) 

5  4  9. ...  Yardmen  (steam  railroad) 

5  5  0. ...         Ticket  and  station  agents 

Express,   post,   telegraph,   and    telephone   (selected    oc- 
cupations) 
5  5  2 ....         Agents  (express  companies) 

Express  messengers  and  railway  mail  clerks 
55  4. ...  Express  messengers 

5  5  5. ...  Railway  mail  clerks 

5  5  7 Mail  carriers 

5  5  9 ....         Telegraph  and  telephone  linemen 

5  6  0 Telegraph  messengers 

5  6  2 Telegraph  operators 

5  6  4. ...         Telephone  operators 

Other  transportation  pursuits 

Foremen  and  overseers  (n.  o.  s.1) 

5  6  6 Road  and  street  building  and  repairing 

5  6  7 Telegraph  and  telephone  companies 

5  6  8 Water  transportation 

5  6  9 Other  transportation 

1  Not  otherwise  specified. 


292  CAUSES  OF  DEATH 

Symbol.  Occupation  and  occupation  group. 

Transportation  —  (Continued) 

Inspectors 
5  7  0 ....  Steam  railroad 

5  7  1 Street  railroad 

5  7  2 ....  Other  transportation 

laborers  (n  o.  s.1) 

5  7  5 ....  Road  and  street  building  and  repairing 

5  7  6. ...  Street  cleaning 

5  7  7 ....  Other  transportation 

Proprietors,  officials,  and  managers  (n.  o.  s.1) 
5  8  0 ....  Telegraph  and  telephone  companies 

5  8  1 ....  Other  transportation 

Other  occupations  (semiskilled) 
5  8  5 ....  Steam  railroad 

5  8  6 Street  railroad 

5  8  7 ....  Other  transportation 

Trade 

Bankers,  brokers,  and  money  lenders 

6  0  0 ....         Bankers  and  bank  officials 

60  1 ....  Commercial  brokers  and  commission  men 

6  0  2 ....  Loan  brokers  and  loan  company  officials 

603 Pawnbrokers 

6  04 Stockbrokers 

6  0  5 ....  Brokers  not  specified  and  promoters 

6  1  1 ....     Clerks  in  stores 

6  1  3 ....     Commercial  travelers 

6  1  5 ....     Decorators,  drapers,  and  window  dressers 

Deliverymen 

6  2  0 ....         Bakeries  and  laundries 
622 Stores 

Floorwalkers,  foremen,  and  overseers 
6  2  4 ....  Floorwalkers  and  foremen  in  stores 
6  2  5. ...  Foremen,  warehouses,  stockyards,  etc. 

1  Not  otherwise  specified. 


OCCUPATIONS  293 

Svmbol  Occupation  and  occupation  group. 

Trade  —  (Continued) 
6  2  7 ....     Inspectors,  gaugers,  and  samplers 

Insurance  agents  and  officials 

6  3  0 Insurance  agents 

6  3  1 ....         Officials  of  insurance  companies 

Laborers  in  coal  and  lumberyards,  warehouses,  etc. 

6  3  3 Coal  yards 

6  3  4 Elevators 

6  3  5. ...         Lumberyards 

6  3  6 Stockyards 

637 Warehouses 

6  4  0. ...     Laborers,  porters,  and  helpers  in  stores 
6  4  2 Newsboys 

Proprietors,  officials,  and  managers  (n.  o.  s.1) 

6  4  4 Employment  office  keepers 

6  4  5. ...         Proprietors,  etc.,  elevators 

6  4  6. ...         Proprietors,  etc.,  warehouses 

6  4  7 Other  proprietors,  officials,  and  managers 

6  5  0 Real  estate  agents  and  officials 

6  5  5 Retail  dealers 

Salesmen  and  saleswomen 
6  6  3 ....         Auctioneers 
6  6  4. ...         Demonstrators 
6  6  5. ...         Sales  agents 
6  6  6 Salesmen  and  saleswomen  (stores) 

6  6  8 Undertakers 

6  7  7 Wholesale  dealers,  importers,  and  exporters 

Other  pursuits  (semiskilled) 

6  8  6 Fruit  graders  and  packers 

6  8  7 Meat  cutters 

6  8  8 Other  occupations 

1  Not  otherwise  specified. 


294  CAUSES  OF  DEATH 

Symbol.  Occupation  and  occupation  group. 

Public  Service  (not  Elsewhere  Classified) 
7  0  0.  ...     Firemen  (fire  department) 
7  0  2.  ...     Guards,  watchmen,  and  doorkeepers 

Laborers  (public  service) 
7  0  6.  ...         Garbage  men  and  scavengers 
7  0  7.  ...         Other  laborers 

Marshals,  sheriffs,  detectives,  etc. 

7  1  0 Detectives 

7  1  1 ....         Marshals  and  constables 

7  1  2.  ...         Probation  and  truant  officers 

7  1  3 Sheriffs 

Officials  and  inspectors  (city  and  county) 
7  1  5 ....         Officials  and  inspectors  (city) 
7  1  6 ....         Officials  and  inspectors  (county) 

Officials  and  inspectors  (state  and  United  States) 

7  2  0 Officials  and  inspectors  (state) 

7  2  1 ....         Officials  and  inspectors  (United  States) 

7  2  5 Policemen 

7  2  7 ....     Soldiers,  sailors,  and  marines 

Other  pursuits 

7  3  0 Life-savers 

7  3  1 ....         Lighthouse  keepers 
7  3  2 ....         Other  occupations 

Professional  Service 
740 Actors 

7  4  2 Architects 

7  4  4. ...     Artists,  sculptors,  and  teachers  of  art 

Authors,  editors,  and  reporters 
7  4  6. ...         Authors 
7  4  7 ....         Editors  and  reporters 
7  5  0 ....     Chemists,  assayers,  and  metallurgists 

Civil  and  mining  engineers  and  surveyors 
7  5  2 ....         Civil  engineers  and  surveyors 
753  ...         Mining  engineers 
7  5  5 ....     Clergymen 

7  5  7 ....     College  presidents  and  professors 
759..         Dentists 


OCCUPATIONS  295 

pmbol.  Occupation  and  occupation  group. 

Professional  Service  —  (Continued) 

Designers,  draftsmen,  and  inventors 

6  0. ...         Designers 

6  1 ...  *         Draftsmen 

6  2 ....         Inventors 

7  6  4 ....  Lawyers,  judges,  and  justices 

7  6  6. ...  Musicians  and  teachers  of  music 

7  6  8. ...  Photographers 

7  7  0 ....  Physicians  and  surgeons 

7  7  2 Showmen 

Teachers 

7  7  4 ....         Teachers  (athletics,  dancing,  etc.) 
7  7  5. . . .         Teachers  (school) 

7  7  7 Trained  nurses 

7  7  9.  ...  Veterinary  surgeons 

7  8  0 ....  Other  professional  pursuits 

Semiprofessional  pursuits 

7  8  1 ....         Abstractors,  notaries,  and  justices  of  peace 
7  8  2 ....         Fortune  tellers,  hypnotists,  spiritualists,  etc. 
7  8  3. ...         Healers  (except  physicians  and  surgeons) 
7  8  4. ...         Keepers  of  charitable  and  penal  institutions 
7  8  5. ...         Officials  of  lodges,  societies,  etc. 
7  8  6. ...         Religious  and  charity  workers 
7  8  7 ....         Theatrical  owners,  managers,  and  officials 
7  8  8 Other  occupations 

7  9  0. ...         Attendants  and  helpers  (professional  service) 

Domestic  and  Personal  Service 

8  0  0.  ...     Barbers,  hairdressers,  and  manicurists 
802 Bartenders 

Billiard  room,  dance  hall,  skating  rink,  etc.,  keepers 
8  0  4. ...         Billiard  and  pool  room  keepers 
8  0  5. ...         Dance  hall,  skating  rink,  etc.,  keepers 

8  1  1 ....  Boarding  and  lodging  house  keepers 

8  1  3 Bootblacks 

8  2  0 ....  Charwomen  and  cleaners 

8  2  2 Elevator  tenders 

8  3  0. ...  Hotel  keepers  and  managers 


296  CAUSES  OF  DEATH 

Symbol.  Occupation  and  occupation  group. 

Domestic  and  Personal  Service  —  (Continued) 

8  3  3.  ...  Housekeepers  and  stewards 

8  3  5 ....  Janitors  and  sextons 

8  4  2 ....  Laborers  (domestic  and  professional  service) 

8  4  4 ....  Launderers  and  laundresses  (not  in  laundry) 

8  4  6.  ...  Laundry  operatives 

8  4  8 ....  Laundry  owners,  officials,  and  managers 

Midwives  and  nurses  (not  trained) 
8  5  4 ....         Midwives 
8  5  5 ....          Nurses  (not  trained) 
8  6  6 ....     Porters  (except  in  stores) 
8  6  8 ....     Restaurant,  cafe,  and  lunch  room  keepers 
8  7  0 ....     Saloon  keepers 

Servants 

8  7  3 ....  Bell  boys,  chore  boys,  etc. 

8  7  4. ...  Chambermaids 

8  7  5 ....  Coachmen  and  footmen 

8  7  6 Cooks 

8  7  7 Other  servants 

8  8  8. ...  Waiters 

Other  pursuits 

8  9  5. ...  Bathouse  keepers  and  attendants 

8  9  6 ....  Cemetery  keepers 

8  9  7. ...  Cleaners  and  renovators  (clothing,  etc.) 

8  9  8. ...  Umbrella  menders  and  scissors  grinders 

8  9  9 ...  Other  occupations 

Clerical  Occupations 

Agents,  canvassers,  and  collectors 

9  5  5...,         Agents 

9  5  6. ...         Canvassers 

9  5  7 Collectors 

9  6  6 Bookkeepers,  cashiers,  and  accountants 

Clerks  (except  clerks  in  stores) 
9  7  6. ...         Shipping  clerks 
9  7  7 Other  clerks 

Messenger,  bundle,  and  office  boys l 

9  8  7 Bundle  and  cash  boys  and  girls 

9  8  8. ...         Messenger,  errand,  and  office  boys 
9  9-9 Stenographers  and  typewriters 

1  Except  telegraph  and  telephone  messengers. 


EXERCISES  AND  QUESTIONS  297 

Nosology  not  an  exact  science.  —  The  following  reported 
causes  of  death  will  enable  the  student  to  decide  whether 
or  not  nosology  is  an  exact  science: 

"Went  to  bed  feeling  well,  but  woke  up  dead." 
"  Died  suddenly  at  the  age  of  103.     To  this  time  he  bid  fair  to  reach 
a  ripe  old  age." 

" Deceased  had  never  been  fatally  sick." 

."Last  illness  caused  by  chronic  rheumatism,  but  was  cured  before 
death." 

"  Died  suddenly,  nothing  serious." 

"While  cranking  his  automobile  sustained  what  is  technically  known 
as  a  colles  fracture  of  the  right  rib." 
"Kick  by  horse  showed  on  left  kidney." 

"Chronic  disease." 

"Deceased  died  from  blood  poison  caused  by  a  broken  ankle,  which 
is  remarkable,  as  the  automobile  struck  him  between  the  lamp  and  the 
radiator." 
."Death  caused  by  five  doctors." 

"Delicate  from  birth." 

"Artery  lung  busted." 

"Collocinphantum." 

"Typhoid  fever,  bronchitis,  pneumonia  and  a  miscarriage." 
—  "  Vital  Statistics." 

EXERCISES  AND    QUESTIONS 

1.  What  does  Van  Buren  mean  by  the  "Will-o'-the-wisp"  of  the 
statistics  of  causes  of  death?     [See  Am.  J.  P.  H.,  Dec.  1917,  p.  1016.] 

2.  What  changes  have  taken  place  in  the  nomenclature  of  "  Tuber- 
culosis," during  the  last  century? 

3.  Give  ten  examples  of  joint  causes  of  death,  indicating  in  each 
case  which  is  primary  and  which  secondary. 

4.  What  preparations  are  being  made  to  revise  the  present  Inter- 
national List  of  Causes  of  Death? 

5.  Select  the  appropriate  cause  of  death  for  statistical  report  from 
the  following  joint  causes  of  death,  and  give  reason  for  your  selection. 

a.  Broncho-pneumonia  and  measles. 

b.  Infantile  diarrhoea  and  convulsions. 

c.  Scarlet  fever  and  diphtheria. 


298  CAUSES  OF  DEATH 

d.  Nephritis  and  scarlet  fever. 

e.  Pulmonary  tuberculosis  and  puerperal  septicemia. 
/.  Typhoid  fever  and  pneumonia. 

g.  Pericarditis  and  appendicitis. 

h.  Cirrhosis  and  angina  pectoris. 

i.  Saturnism  and  peritonitis. 

j.  Old  age  and  bronchitis. 


CHAPTER  IX 
ANALYSIS   OF  DEATH-RATES 

Reasons  for  Analyzing  a  Death-rate.  —  We  have  now 
covered  the  principal  methods  used  in  the  simpler  forms  of 
statistical  study.  We  have  seen  the  futility  of  using  general 
death-rates  for  comparing  the  mortality  of  different  places. 
We  have  learned  how  to  compute  specific  rates  for  groups 
and  classes,  particular  rates  for  different  diseases  and  special 
rates  of  various  kinds.  Let  us  now  put  these  ideas  together 
and  say  that  the  way  to  use  a  general  death-rate  is  to  analyze 
it.  Taken  by  itself  it  means  very  little,  but  if  properly 
analyzed  it  will  yield  us  useful  information. 

Two  Methods  of  Analysis.  —  There  are  two  methods  "of 
analyzing  a  general  death-rate. 

One  is  to  sub-divide  the  numerator  of  the  fraction  into 
classes  and  groups,  leaving  the  denominator  of  the  fraction 
unchanged.  The  total  population  at  mid-year  is  taken  as 
the  denominator  of  the  fraction.  This  is  sometimes  done  in 
separating  all  of  the  deaths  in  a  year  according  to  months 
and  dividing  each  by  the  total  population.  It  has  the  ad- 
vantage that  the  sum  of  all  the  parts  is  equal  to  the  whole. 
In  the  case  mentioned  the  sum  of  all  the  monthly  rates  gives 
the  yearly  rate.  It  has  the  disadvantage  that  the  figures 
cannot  be  compared  or  any  standard  easily  carried  in  the 
mind. 

Another  and  better  method  is  to  sub-divide  both  the 
numerator  and  denominator  into  classes  and  groups,  that  is, 
to  find  their  specific  rates.  Here  the  sum  of  the  rates 

299 


300 


ANALYSIS  OF  DEATH-RATES 


resulting  from  the  separation  does  not  equal  the  whole.  The 
weighted  average  of  the  constituent  rates  will,  however, 
equal  the  whole. 

Let  us  take  a  simple  example: 

In  1910  in  Massachusetts  there  were  the  following  popu- 
lations and  deaths  classified  by  sex. 


TABLE  72 
POPULATION  AND  DEATHS:  MASSACHUSETTS 


Population. 

Deaths. 

(1) 

(2) 

(3) 

Males  

1,655,248 

28,259 

Females  

1,711,168 

26,148 

Total  

3,366,416 

54,407 

According  to  the  first  method  of  analysis  the  partial  rates 
would  be  28,259  -^  3366  =  8.4  for  males,  and  26,148  -f- 
3366  =  7.7  for  females,  the  sum  being  16.1,  which  is  the 
same  as  dividing  54,407  by  3366,  i.e.,  16.1  per  1000. 

According  to  the  second  method  the  specific  rate  for  males 
is  28,259  -s-  1655  =  17.1,  and  for  females,  26,148  -5-  1711  = 
15.3.  In  this  case  the  weighted  average  would  be  (17.1  X 
1655  +  15.3  X  1711)  •*-  3366  =  16.1  per  1000.  The  ad- 
vantage of  this  second  method  is  obvious,  as  one  may  readily 
compare  the  rate  of  17.1  for  males,  and  that  of  15.3  for 
females,  with  16.1,  the  death-rate  for  the  entire  popula- 
tion. In  other  words,  this  method  of  analysis  gives  us  a 
chance  to  compare,  and  that  is  a  prime  object  of  statistical 
study. 

Useful  subdivisions.  —  For  the  purpose  of  analyzing  a 
general  death-rate  we  may  subdivide  the  area  geographically, 
finding  the  specific  death-rate  for  each  part.  A  state  may 


ANALYSIS  OF  A  DEATH-RATE   FOR  A  STATE     301 

be  subdivided  into  counties,  boroughs,  cities  and  towns;  or 
into  urban  and  rural  districts.  A  large  city  may  be  divided 
into  wards,  precincts  or  blocks.  The  subdivisions  must  be 
so  chosen  that  both  the  population  and  the  deaths  may  be 
obtained  for  each  one.  This  often  limits  the  comparison  to 
political  subdivisions.  Those  who  take  the  census  and  those 
who  keep  the  death  records  should  get  together  and  see  that 
.the  geographical  subdivisions  correspond.  Having  made 
these  subdivisions  and  obtained  the  rates  for  each,  the  results 
should  be  arrayed  and  studied  by  the  statistical  method 
described  in  a  later  chapter. 

We  may  subdivide  the  year  into  seasons,  months,  weeks,  or 
even  days  and  ascertain  the  specific  death-rate  for  each  sub- 
division. These  results  should  be  arranged  for  chronological 
study,  and  for  comparing  the  results  for  similar  seasons  or 
months  for  different  years. 

We  may  subdivide  the  population  by  sex,  by  nationality, 
by  occupation,  and  in  all  sorts  of  ways. 

We  may  subdivide  the  deaths  according  to  cause,  using 
either  individual  causes  or  classes  of  causes. 

And  finally  we  may  use  these  various  separations  in  com- 
bination with  each  other. 

Example  of  the  analysis  of  a  general  death-rate  for  a 
state.  —  To  give  a  complete  example  of  an  analysis  of  the 
general  death-rate  of  a  state  would  require  a  small  volume. 
A  few  hints  may  be  given  by  asking  a  number  of  questions 
in  regard  to  Massachusetts  for  the  year  1910. 

According  to  the  73d  Registration  Report  the  general 
death-rate  for  the  state  was  16.1. 

Q.   Was  the  death-rate  uniform  throughout  the  state? 

The  answer  is  obtained  by  finding  the  rate  for  each  county 
and  placing  them  in  array,  that  is,  in  order  of  magnitude. 
The  result  is  as  follows: 


302 


ANALYSIS  OF  DEATH-RATES 


TABLE  73 
DEATH-RATES  BY  COUNTIES:    MASSACHUSETTS,   1910 


County. 

General  death- 
rate. 

County. 

General  death- 
rate. 

(1) 

(2) 

(1) 

(2) 

Norfolk    

13  3 

Essex  

15  9 

Plymouth  

14  2 

Bristol  

16  3 

Middlesex.  .  . 

15  4 

Hampden  

16  8 

Franklin   .... 

15.5 

Suffolk  

17.0 

Worcester 

15  6 

Barnstable 

18  1 

Berkshire 

15  6 

Dukes 

19  1 

H  amps  hire 

15  7 

Nantucket 

20  2 

Q.  What  was  the  median  death-rate  for  the  different 
counties,  that  is,  the  rate  for  the  county  in  the  middle  of  the 
list? 

It  was  15.8,  i.e.,  between  15.7  and  15.9. 

Q.  Why  is  this  median  rate  lower  than  16.1,  the  rate  for 
the  entire  state? 

The  more  populous  counties  have  death-rates  relatively 
high  and  this  brings  up  the  average.  An  average  of  these 
county  rates  weighted  according  to  their  population  would 
give  16.1. 

Q.  Why  was  the  rate  for  Nantucket  county  so  much 
higher  than  that  for  Norfolk? 

In  order  to  answer  this  question  intelligently  we  need  to 
find  out  when  the  deaths  occurred  (seasonal  distribution), 
where  the  deaths  occurred  (geographical  distribution),  who 
died  (distribution  by  sex,  age,  nationality),  what  was  the 
cause  of  death.  Knowing  these  facts  we  should  then  seek 
to  correlate  them  with  controllable  conditions. 

As  a  rule  a  county  is  not  a  good  geographical  unit  for 
such  a  study  as  it  is  difficult  to  get  the  facts.  A  city  is 
better. 


COMPARISON  OF  DEATH-RATES  OF  TWO  CITIES     303 

Comparison  of  the  death-rates  of  two  cities.  —  In  1910 
the  general  death-rates  of  the  cities  of  Massachusetts  which 
had  populations  exceeding  50,000  were  as  follows: 


TABLE  74 

DEATH-RATES  OF  CERTAIN  CITIES  IN  MASSACHUSETTS 

1910 


City. 

General  death- 
rate. 

City. 

General  death- 
rate. 

(1) 

(2) 

(1) 

(2) 

Brockton 

12  3 

Boston 

17  2 

Lynn 

13  1 

Holyoke 

17  7 

Somerville  
Cambridge  .... 

13.4 
15  0 

Lawrence  
Fall  River       

17.7 
18.4 

Springfield  

16  6 

New  Bedford  

18.6 

Worcester.  .  . 

16  9 

Lowell  

19.7 

Q.  Why  was  the  death-rate  so  much  higher  in  Lowell  than 
in  Brockton? 

We  naturally  look  first  to  differences  in  age  and  sex  dis- 
tribution. The  U.  S.  Census  gives  us  the  following  infor- 
mation: 

TABLE  75 

AGE  AND  SEX  DISTRIBUTION  OF  POPULATION  IN 
BROCKTON  AND  LOWELL,  MASS. 


Brockton. 

Lowell. 

(1) 

(2) 

(3) 

Per  cent  of  population  under  10  years 
Male  ... 

8.8 

9.3 

Female  

8.6 

9.3 

Per  cent  of  population  over  45  years 
Male   . 

10  1 

9  2 

Female 

10  6 

10.8 

304  ANALYSIS  OF  DEATH-RATES 

These  differences  are  not  striking,  except  that  Lowell  has 
a  somewhat  larger  percentage  of  children  under  ten  years  of 
age.  How  about  infants?  There  is  not  much  difference. 
In  Brockton  the  infant  population  was  2.15  per  cent  of  the 
total,  in  Lowell,  2.19  per  cent.  The  sex  differences  are  not 
great  except  that  in  Lowell'  in  the  age-group  15-44  years 
there  are  more  females  than  males,  while  in  Brockton  the 
numbers  are  about  alike. 

Let  us  next  turn  to  nationality.  Here  we  find  a  great 
difference.  In  Brockton,  72  per  cent  of  the  population  were 
native  white  and  27  per  cent  foreign-born  white,  but  in 
Lowell  only  59  per  cent  were  native  white  while  40  per  cent 
were  foreign-born  white.  Pursuing  this  further  we  find  that 
in  Lowell  the  foreign-born  whites  were  made  up  of  French 
Canadians, 28.3  per  cent;  Irish,  23.0  per  cent;  English,  10.5 
per  cent;  Canadians  other  than  French,  9.3  per  cent;  Greeks, 
8.7  per  cent.  The  corresponding  figures  for  Brockton  are 
not  given  in  the  census  report. 

With  these  fundamental  differences  in  mind  we  must  next 
turn  to  industrial  conditions,  living  conditions,  etc.  Brock- 
ton is  a  shoe  city,  Lowell  a  textile  city.  The  housing  condi- 
tions of  the  working  classes  in  Brockton  are  better  than  in 
Lowell.  These  matters  should  be  studied  in  detail. 

But  what  of  the  causes  of  death?  The  annual  report  of 
the  State  Board  of  Health  shows  that  the  death-rate  for  pneu- 
monia was  118  per  100,000  in  Brockton,  but  210  in  Lowell; 
tuberculosis  88  and  137  respectively,  diarrhea  and  cholera 
morbus  23  and  184.  This  last  is  a  very  important  difference. 

Turning  to  the  age  distribution  of  deaths  we  find  that  in 
Brockton  18.5  per  cent  of  the  deaths  were  infants,  in  Lowell 
25.2  per  cent.  Evidently  the  large  number  of  infant  deaths, 
the  large  numbers  of  deaths  from  dysentery  and  the  large 
foreign-  population  in  Lowell  point  to  certain  environmental 
conditions  which  influence  mortality. 


"RATES"  NOT  THE  ONLY  METHOD  OF  COMPARISON    305 


In  order  to  get  these  facts  it  was  necessary  to  consult  the 
State  Registration  Report,  the  Annual  Report  of  the  State 
Board  of  Health  and  the  Census  Report.  The  annual 
reports  of  the  local  boards  of  health  should  have  contained 
these  essential  data;  in  fact  they  should  have  contained  the 
following  specific  death-rates  for  1910: 

TABLE  76 

SPECIFIC  DEATH-RATES  BY  AGE-GROUPS  FOR  BROCKTON 
AND  LOWELL:    1910 


Specifie  death-rates  per  1000. 

Age-group. 

Brockton. 

Lowell. 

Male. 

Female.     ' 

Male. 

Female. 

(1) 

(2) 

(3) 

(4) 

(5) 

0-1 

123.0 

101.0 

286.0 

237.0 

1-4 

8.0 

13.0 

31.0 

35.0 

5-9 

3.5 

6.5 

5.2 

4.6 

10-14 

2.1 

3.0 

1.6 

2.7 

15-19 

4.0 

3.2 

4.7 

3.1 

20-24 

3.1 

2.6 

5.2 

5.0 

25-34 

3.9 

6.0 

7.5 

6.8 

35-44 

4.7 

4.3 

9.8 

10.7 

45-G4 

18.4 

11.8 

24.0 

23.0 

65- 

106.0 

90.0 

99.0 

95.0 

These  figures  show  directly  that  the  infant  death-rate  was 
much  higher  in  Lowell  than  in  Brockton,  that  the  death-rate 
for  young  children  was  also  higher.  This  would  point  at 
once  to  home  environment.  But  the  rates  were  also  higher 
in  Lowell  for  the  middle-age  groups,  which  would  point  to 
greater  industrial  hazards  there. 

"  Rates  "  not  the  only  method  of  comparison.  —  So 
much  has  been  said  about  rates  and  specific  rates  that  there 
is  danger  that  the  student  may  come  to  think  of  them  as 


306 


ANALYSIS  OF  DEATH-RATES 


the  only  method  of  statistical  comparison.    That  is  far  from 
being  the  case. 

The  seasonal  changes  in  mortality  may  be  shown  in  three 
ways,  each  of  which  has  its  use.  In  Massachusetts  the 
general  death-rate  for  1910  was  16.1  per  1000.  It  varied 
seasonally  as  follows: 

TABLE  77 

SEASONAL  DISTRIBUTION  OF  MORTALITY 
Massachusetts,   1910 


Month. 

Death-rate. 

Percentage  of 
total  deaths. 

Ratio  of  monthly 
deaths  to  average 
number  for  each 
month. 

(1) 

(2) 

(3) 

(4) 

January  

17.1 

8.9 

106 

February  

17.1 

8.1 

106 

March  

17.8 

9.5 

110 

April 

17  2 

8  8 

107 

May 

15  2 

8  0 

94 

June   . 

14  4 

73 

89 

July 

17  2 

9  0 

107 

August  .         

16  6 

8.7 

103 

September  

15.8 

8.0 

98 

October  
November 

14.7 

14  8 

7.7 
7  5 

91 
92 

December  

16.2 

8.5 

101 

Year  

16.1 

100.0 

100 

Column  (2)  gives  the  death-rate  for  each  month  as  compared 
with  the  yearly  rate.  Columns  (3)  and  (4)  are  most  useful 
in  comparing  one  year  with  another.  They  do  not  involve 
population,  an  uncertain  factor  in  all  but  the  census  years, 
but  on  the -other  hand  a  change  in  one  month  affects  the 
figures  in  all  the  other  months. 


EXERCISES  AND  QUESTIONS  307 

EXERCISES  AND   QUESTIONS 

1.  Make  a  statistical  analysis  of  the  general  death-rates  of  Boston 
and  Baltimore  for  the  year  1910. 

2.  Make  a  statistical  analysis  of  the  general  death-rates  of  Chicago 
and  New  Orleans  for  the  year  1910. 

3.  Make  a  statistical  analysis  of  the  general  death-rates  of  other  cities 
to  be  assigned  by  instructor. 

4.  Find  the  median  death-rate  for  the  counties  of  New  York  state 
for  1910. 

5.  Compare  the  seasonal  mortalities  of  San  Francisco  and  Boston 
for  1910,  using  several  different  methods  of  statement. 


CHAPTER  X 
STATISTICS   OF  PARTICULAR  DISEASES 

In  studying  particular  diseases  we  commonly  use  four 
ratios  which,  though  described  in  different  ways,  may  be 
distinguished  by  the  terms,  (a)  mortality  rate;  (6)  propor- 
tionate mortality;  (c)  morbidity  rate  and  (d)  fatality  or 
case  fatality.  In  addition  to  these  ratios  the  number  of 
cases  of  a  particular  disease  may  be  arranged  in  groups  and 
classes,  by  age,  sex,  nationality,  occupation,  date  of  onset 
and  in  other  ways  without  using  ratios;  and  the  same  is 
true  of  deaths  from  a  particular  disease. 

Mortality  rate.  —  The  mortality  rate  for  a  particular 
disease  is  obtained  by  dividing  the  number  of  deaths  from 
that  disease  by  the  mid-year  population  expressed  in  hundred 
thbusands. 

Proportionate  Mortality.  —  The  proportionate  mortality 
of  a  particular  disease  is  the  per  cent  which  the  number  of 
deaths  from  that  disease  is  of  the  total  number  of  deaths 
from  all  causes.  The  interval  of  time  is  usually  taken  as 
one  year,  but  shorter  periods  may  be  used.  This  method  is 
sometimes  spoken  of  as  the  percentage  of  mortality,  or 
per  cent  distribution. 

Percentages  of  mortality  are  not  as  commonly  published 
as  they  were  some  years  ago.  They  do  not  mvolve  the 
population,  hence  they  are  especially  useful  where  the  popu- 
lation is  not  known  or  cannot  be  correctly  estimated.  Since 
the  custom  of  estimating  population  by  a  uniform  system 
has  become  general  there  has  been  less  need  for  considering 

308 


INACCURACY  OF  MORBIDITY  AND  FATALITY  RATES  309 

the  percentage  of  mortality.  A  theoretical  disadvantage  of 
the  method  is  the  fact  that  the  number  of  deaths  from  the 
particular  disease  appears  in  both  the  numerator  and  the 
denominator  of  the  fraction;  that  is,  the  number  of  deaths 
from  the  particular  disease  helps  to  make  up  the  total 
number  of  deaths. 

Morbidity  rate.  —  The  morbidity  rate  is  the  ratio  between 
the  number  of  cases  of  a  particular  disease  in  a  year  and  the 
mid-year  population  expressed,  in  thousands,  or  better  in 
hundred  thousands.  It  is  sometimes  called  the  "case  rate." 
The  morbidity  rate  is  very  useful  in  epidemiological  investi- 
gations. It  is  usually  based  on  the  entire  population,  but  just 
as  in  the  case  of  death-rates,  or  mortality  rates,  from  particular 
diseases  it  may  be  computed  for  specific  age-groups  or  classes. 

Fatality.  —  The  fatality  of  a  disease  is  the  ratio  between 
the  number  of  deaths  and  the  number  of  cases.  It  is  best 
expressed  as  a  percentage.  The  fatality  of  any  disease  is 
far  from  being  the  same  at  all  ages. 

Example.  —  In  1915  the  population  of  Cambridge,  Mass., 
was  108,822;  the  total  number  of  deaths  from  all  causes 
1460;  the  number  of  cases  and  deaths  from  scarlet  fever 
were  379  and  5,  respectively.  From  these  facts  we  have  the 
following  rates  and  ratios: 

General  death-rate,  1460  ^  108.822  =  13.45  per  1000. 
Scarlet-fever,  mortality  rate,  5  -r-  1.08822  =  4.6  per  100,000. 
Scarlet-fever,  proportionate  mortality,  5  -f-  14.60  =  0.34  per  cent. 
Scarlet-fever,  morbidity  rate,  379  -r-  1.08822  =  347  per  100,000. 
Scarlet-fever,  fatality,  5  -T-  379  =  1.32  per  cent. 

Inaccuracy  of  morbidity  and  fatality  rates.  —  It  must 
not  be  forgotten  that  rates  for  morbidity  are  based  on  re- 
ported cases  and  that  not  all  cases  are  reported.  Nearly  all 
morbidity  rates  are  too  low.  It  follows  therefore,  that 
nearly  all  fatality  percentages  are  too  high.  In  the  case  of 
typhoid-fever,  for  example,  a  comparison  of  deaths  and 


310 


STATISTICS  OF  PARTICULAR  DISEASES 


reported  cases,  has  led  to  the  popular  idea  that  the  fatality  is 
about  10  per  cent,  that  is,  one  death  for  every  ten  cases. 
But  in  a  number  of  epidemics,  where  the  cases  were  accurately 
obtained  by  a  house  to  house  canvas,  it  has  been  found  that 
there  were  from  twelve  to  fifteen  cases  for  each  death,  that 
is,  the  fatality  was  only  about  7  per  cent. 

It  is  interesting  to  see  how  an  epidemic  of  typhoid  fever 
will  result  in  an  increased  proportion  of  cases  being  reported. 
In  Cleveland,  Ohio,  in  the  year  1902  there  were  but  3.7  times 
as  many  reported  cases  as  deaths,  but  the  following  year, 
when  a  severe  epidemic  occurred,  there  were  7.3  times  as 
many  reported  cases  as  deaths.  If  the  figures  for  1902  had 
been  correct  it  would  have  meant  a  fatality  of  27  per  cent, 
which  is  most  unlikely. 

Causes  of  death  in  Massachusetts.  —  In  1915  the  prin- 
cipal causes  of  death  in  Massachusetts  were  as  follows. 
They  are  arranged  according  to  the  Abridged  International 

List. 

TABLE  78 

PRINCIPAL  CAUSES  OF  DEATH  IN  MASSACHUSETTS 


Rank. 

Cause  of  death. 

Per  cent  of 
mortality. 

(1) 

(2) 

(3) 

1 

Pneumonia  (92)  

8  8 

2 

Tuberculosis  of  the  lungs  (28,  29)  

8  3 

3 

Organic  diseases  of  the  heart  (79)  

7.4 

4 

Diarrhea  and  enteritis  (104)  

6.9 

5 
6 

Congenital  debility  and  malformations  (150,  151).  . 
Cerebral  hemorrhage  and  softening  (64,  65) 

6.8 
6  1 

7 
8 
9 

Cancer  and  other  malignant  tumors  (39-45)  
Acute  nephritis  and  Bright's  disease  (119,  120)  
Other  diseases  of  respiratory  system  (86-88,  91, 
93-98) 

5.6 
5.6 

4  8 

10 

Violent  deaths,  suicide  excepted  (164—186)  

4.4 

It  will  be  seen  that  these  ten  causes  account  for  nearly  two- 
thirds  of  all  the  deaths. 


STUDY  OF  TUBERCULOSIS  BY  AGE  AND  SEX     311 

The  ten  most  important  causes  of  death  for  the  U.  S. 
registration  area  in  1914  were  not  placed  in  the  same  order, 
but  were  as  follows: 

TABLE  79 
PRINCIPAL  CAUSES  OF  DEATH:  UNITED  STATES,  1915 


Rank. 


Cause  of  death. 


(1) 


(2) 


1 
2 
3 
4 
5 
6 
7 
8 
9 
10 


Organic  diseases  of  the  heart  (79) 

Tuberculosis  of  the  lungs  (28,  29) 

Bright's  disease  (119,  120) 

Pneumonia  (92) 

Violent  deaths  (164-186) 

Cancer  (39-45) 

Cerebral  hemorrhage  (64,  65) 

Congenital  debility  and  malformations  (150,  151) 

Diarrhea  and  enteritis  (104) 

Bronchitis  (89,  90) 


The  proportionate  mortality  differs  more  or  less  in  different 
places.  It  is  not  the  same  for  the  two  sexes.  It  differs 
greatly  at  different  ages.  It  is  not  the  same  at  all  seasons. 
It  is  different  to-day  from  what  it  was  a  generation  ago.  The 
control  of  communicable  diseases  has  considerably  altered 
the  relative  importance  of  the  different  causes  of  death. 

Study  of  tuberculosis  by  age  and  sex.  —  In  attempting  to 
study  any  particular  disease  in  order  to  determine  its  relation 
to  age  and  sex  one  will  be  surprised  to  find  how  difficult  it  is 
to  get  a  complete  statement  of  the  necessary  facts  for  any 
given  place.  Obviously  we  need  to  have  both  the  cases 
and  deaths  classified  by  age  and  sex,  and  we  also  need  the 
population  and  the  deaths  from  all  causes  arranged  by  sex 
and  according  to  the  same  age  grouping.  If  we  attempt -to 
use  the  U.  S.  Census  reports  we  find  that  no  data  for  cases 
are  given;  if  we  attempt  to  use  the  state  board  of  health 


312  STATISTICS  OF  PARTICULAR  DISEASES 

reports  we  may  find  that  the  deaths  are  classified  by  age  and 
sex,  but  that  only  the  total  numbers  are  given  for  cases;  in 
some  city  board  of  health  reports  we  may  find  cases  and 
deaths  duly  classified  but  no  populations  given  for  the 
corresponding  groups  and  classes.  As  an  illustration  of  un- 
satisfactory current  practice  let  us  study  the  statistics  of 
tuberculosis  for  the  city  of  Cambridge,  Mass.,  for  the  year 
1915.  The  data  in  the  following  table  were  taken  from  the 
annual  report  of  the  local  board  of  health,  except  the  popu- 
lation statistics,  which  were  taken  from  the  state  census  of 
that  year.  These  data  are  more  than  ordinarily  complete, 
yet  they  are  not  satisfactory,  due  chiefly  to  incomplete 
reports  of  cases.  It  may  be  assumed  that  the  numbers  of 
deaths  are  reasonably  precise,  yet  they  do  not  strictly 
represent  local  conditions  as  they  include  deaths  in  hospitals. 

The  numbers  of  cases  and  deaths  are  small  and  this  also 
makes  the  derived  rates  subject  to  erratic  fluctuations. 

The  fundamental  data  are  given  in  columns  (2)  to  (9),  the 
derived  figures  in  the  subsequent  columns.  Column  (10) 
was  obtained  from  columns  (2)  and  (8);  column  (12)  from 
column  (8) ;  column  (14)  from  columns  (6)  and  (2) ;  column 
(16)  from  column  (6);  column  (18)  from  columns  (6)  and  (4); 
column  (20)  from  columns  (6)  and  (8). 

If  we  take  the  figures  at  their  face  value  we  notice  first 
that  both  the  morbidity  and  mortality  rates  are  high  in 
infancy  and  low  in  childhood.  The  male  morbidity  rate 
reaches  its  highest  point  in  age  group  30-39  years,  but  the 
male  mortality  rate  is  highest  between  40  and  50.  In  females 
the  morbidity  rate  rises  earlier  and  is  highest  in  age-group 
20-29.  The  highest  female  mortality  rate  is  also  found  in 
the  same  group.  Forty  per  cent  of  all  the  cases  and  37.9  per 
cent  of  all  the  deaths  from  tuberculosis  among  females  oc- 
curred between  the  ages  of  twenty  and  thirty. 

If  we  study  the  figures  for  proportionate  mortality  .we  see 


STUDY  OF  TUBERCULOSIS  BY  AGE  AND  SEX     313 

TABLE  80 
CAMBRIDGE,   MASS.,   1915 

Statistics  of  Tuberculosis  (28-35)  Cases  and  Death,  Arranged  by 
Age  and  Sex 


Age- 
group. 

Population. 

Deaths,  all 
causes. 

Tuberculosis 
•    Deaths. 

Tuberculosis 
Cases. 

1 

OJ 

I 

1 

1 

• 

1 

£ 

J5 

1 

£ 
n 

£ 

ai 
"3 

s 
£ 

(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

(7) 

(8) 

(9) 

0-1 
1-4 
5-9 
10-14 
15-19 
20-29 
30-39 
40-49 
50-59 
60- 
Total 

1,114 
4,161 
4,996 
4,488 
4,569 
10,424 
8,334 
6,552 
4,133 
3,224 

1,080 
4,120 
5,000 
4,533 
4,901 
11,326 
9,190 
7,177 
4,823 
4,678 

138 
38 
13 

7 
22 
44 
64 
80 
88 
229 

105 
40 
13 
6 
12 
51 
43 
76 
85 
306 

0 
2 
0 
1 
9 
23 
29 
32 
13 
10 

1 
1 
1 
1 

7 
31 
19 
10 
6 
5 

1 

6 
4 
4 
9 
40 
49 
31 
14 
9 

1 

1 

5 
0 
17 
50 
31 
9 
8 
3 

51,995 

56,808 

723 

737 

119 

82 

167 

125 

Age- 
group. 

Morbidity 
(case), 
rate  per 
100,000. 

Percentage 
distribution 
of  cases. 

Mortality 
(death) 
rate. 

Percentage 
distribution 
of  deaths. 

Proportion- 
ate mortal- 
ity, per  cent. 

Fatality, 
per  cent. 

.2 

i 
I 

J> 

03 
3 

i 

s 

i 

1 

• 

•a 

1 

1 

d 

"3 

£ 

4 

a 
3 

9 

"a 
I 

1 

0) 

13 
1 
(21) 

(1) 

(10) 

an 

(12) 

(13) 

(14) 

(15) 

(16) 

(17) 

(18) 

(19) 

(20) 

0-1 
1-4 
5-9 
10-14 
15-19 
20-29 
30-39 
40-49 
50-59 
60- 
Total 

90 
144 
80 
89 
197 
383 
588 
473 
339 
279 
321 

93 
41 
100 
0 
347 
441 
337 
125 
166 
64 
220 

0.6 
3.6 
2.4 
2.4 
5.4 
23.8 
29.4 
18.6 
8.4 
5.4 

0.8 
0.8 
4.0 
0.0 
13.6 
40.0 
24.8 
7.2 
6.4 
2.4 

0 

48 
0 
22 
197 
220 
348 
488 
315 
310 

93 
41 
20 
26 
143 
274 
207 
139 
124 
107 

0 
1.7 
0 
0.8 
7.6 
19.3 
24.4 
26.9 
10.9 
8.4 

1.2 
1.2 
1.2 
1.2 
8.5 
37.9 
23.2 
12.2 
7.3 
6.1 

0 
5 
0 
14 
39 
52 
45 
40 
15 
4 

1 

3 
8 
17 
58 
61 
44 
13 
7 
2 

0 
33 
0 
25 
100 
57 
59 
103 
92 
111 

100 
100 
20 

41 
62 
61 
111 
75 
167 

100.0 

100.0 

229 

144 

100.0 

100.0 

16.5 

11.1 

71 

66 

314  STATISTICS  OF  PARTICULAR  DISEASES 

that  tuberculosis  caused  16.5  per  cent  of  all  deaths  among 
males  and  11.1  per  cent  of  all  deaths  among  females.  In  age- 
group  20-29  this  disease  caused  nearly  two-thirds  of  all 
deaths  of  females  and  more  than  half  of  all  deaths  of  males. 
In  comparing  the  figures  for  proportionate  mortality  it  should 
be  observed  that  the  age-groups  are  not  of  equal  value 
throughout  the  table;  some  cover  ten  years,  some  five,  one 
covers  four  years,  and  one  only  one  year. 

The  fatality  rates  are  practically  worthless.  Sometimes  the 
number  of  reported  cases  was  less  than  the  number  of  deaths, 
thus  making  the  fatality  rate  higher  than  100  per  cent.  This 
would  be  an  absurdity,  if  we  did  not  know  that  the  tuber- 
culosis deaths  of  one  year  may  represent  cases  of  the  year 
before  or  the  year  before  that.  Tuberculosis  is  a  disease  of 
long  duration,  sometimes  several  years.  The  fatality  of  such 
a  disease  as  this  cannot  be  computed  in  this  way.  Yet 
imperfect  as  these  figures  are  we  can  gather  from  them  the 
main  facts.  We  can  see  that  tuberculosis  is  essentially  a 
disease  of  early  manhood  and  womanhood,  and  at  those  ages 
we  naturally  look  to  working  conditions  as  contributory 
factors.  The  disease  continues  as  an  important  cause  of 
death  up  to  old  age,  especially  among  males. 

If  we  take  the  figures  for  the  U.  S.  Registration  Area  as 
given  in  the  Mortality  Report  for  1914  we  obtain  a  more 
uniform  set  of  figures,  as  they  are  based  on  898,059  deaths 
instead  of  1460  deaths.  (Table  81.)  Here  the  highest 
proportionate  mortality  for  tuberculosis  was  for  age-group 
20-24  years;  for  males  it  was  34.3  per  cent,  for  females  39.2. 
These  figures  are  considerably  lower  than  for  Cambridge. 
The  percentage  distribution  of  tuberculosis  deaths  showed 
a  maximum  in  age-group  20-24  for  females,  and  in  age-group 
25-29  for  males.  The  morbidity,  mortality  and  fatality 
could  not  be  computed  as  no  records  of  cases  and  no  popula- 
tion by  age-groups  were  given  in  the  Mortality  Report. 


DISTRIBUTION  OF   DEATHS  FROM   TUBERCULOSIS      315 


TABLE  81 

DEATHS  FROM  TUBERCULOSIS  OF  THE  LUNGS    (28) 
U.  S.  Registration  Area,  1914,  by  Age  and  Sex 


Age- 

Deaths,  all  causes. 

Deaths  (28) 

Percentage 
distribution. 

Proportionate 
mortality. 

group. 

Male. 

Female. 

Mate. 

Female. 

Male. 

Female. 

Male. 

Female. 

(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

(7) 

(8) 

(9) 

0-4 

118,375 

95,735 

3,416 

2,832 

6.1 

6.9 

2.9 

3.0 

5-9 

10,162 

9,140 

832 

878 

1.5 

2.1 

8.2 

9.6 

10-14 

6,819 

6,054 

702 

1,235 

1.3 

3.0 

10.3 

20.3 

15-19 

10,934 

10,322 

2,719 

3,801 

4.9. 

9.2 

24.8 

36.8 

20-24 

17,516 

15,408 

6,002 

6,061 

10.8 

14  7 

34  3 

39.2 

25-29 

19,407 

16,300 

6,634 

5,795 

11.9 

14.1 

34.0 

35.5 

30-34 

20,212 

15,878 

6,466 

4,701 

ir.e 

11.4 

32.2 

29.7 

35-39 

23,154 

17,155 

6,428 

3,922 

11.5 

9.5 

27.8 

22.9 

40-44 

24,116 

16,803 

5.761 

2,950 

10.3 

7.2 

23.8 

17.6 

45-49 

25,283 

17,779 

<640 

2,172 

8.3 

5.3 

18.3 

12.2 

50-54 

28,809 

20,294 

3,853 

1,679 

6.9 

4.1 

13.4 

8.3 

55-59 

28,896 

21,006 

2,905 

1,388 

5.2 

3.4 

10.1 

6.6 

60-64 

31,255 

24,275 

2,139 

1,217 

3.8 

3.0 

6.8 

5.0 

65-69 

32,728 

27,075 

1,460 

966 

2.6 

2.3 

4.5 

3.6 

70-74 

32,760 

29,109 

929 

777 

1.6 

1.9 

2.8 

2.7 

75-79 

27,365 

26,410 

515 

465 

0.9 

1.1 

1.9 

1.8 

80-84 

19,132 

20,537 

188 

205 

0.3 

0.5 

1.0 

1.0 

85-89 

9,600 

11,447 

48 

57 

0.1 

0.1 

0.5 

0.5 

90-94 

3,129 

4,165 

9 

16 

.... 

0.3 

0.4 

95-99 

704 

1,007 

6 

3 

100- 

179 

288 

1 

2 

Total 

491,416 

406,643 

55,724 

41,179 

100.0 

100.0 

11.4 

10.2 

Seasonal  Distribution  of  deaths  from  tuberculosis.  —  A 

natural  way  of  studying  the  seasonal  distribution  of  deaths 
from  tuberculosis  is  to  subdivide  the  annual  number  of  deaths 
into  the  numbers  which  occurred  each  month  and  then  find 
what  per  cent  each  is  of  the  whole.  It  is  common  to  arrange 
the  results  in  a  horizontal  line  thus: 


316 


STATISTICS  OF  PARTICULAR  DISEASES 


TABLE  82 

SEASONAL  DISTRIBUTION   OF  DEATHS  FROM   TUBER- 
CULOSIS  (28-35) 

U.  S.  Registration  Area,  1914 


1 

1 

J3 
1 

•c 

— 
^ 

>> 

i 

>-» 

>, 
"3 

S 

1 

1 

i 

£ 

H 

(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

(7) 

(8) 

(9) 

(10) 

(11) 

(12) 

(13) 

(14) 

Number  of  deaths.  .  .  . 
Per  cent  of  total  for  the 
year 

7522 
8.9 

7524 
8.9 

8537 
10.5 

8238 
9.8 

7782 
9.2 

6901 
8.1 

6528 
7.6 

6209 
7.4 

6031 

71 

6009 
7.1 

6212 
7.4 

6873 
8.0 

84,366 
100.0% 

These  figures  show  that  the  largest  numbers  of  deaths 
occur  during  the  spring  months,  but  the  difference  between 
winter  and  summer  is  not  great.  It  must  not  be  forgotten 
in  such  a  comparison  as  this  that  the  months  are  of  unequal 
length.  While  the  above  figures  show  that  8.9  per  cent  of 
the  deaths  occurred  in  February  and  10.5  per  cent  in  March 
the  average  number  of  deaths  per  day  was  269  per  day  in 
February  and  275  per  day  in  March.  The  U.  S.  Mortality 
Report,  from  which  these  figures  were  taken,  do  not  dis- 
tribute the  deaths  in  each  month  according  to  age. 

Another  way  of  studying  the  seasonal  distribution  is  to 
find  the  proportionate  mortality  for  tuberculosis  for  each 

month. 

TABLE  83 

PROPORTIONATE  MORTALITY  FROM  TUBERCULOSIS 
BY  MONTHS   (28-35) 

U.  S.  Registration  Area,  1914 


c 

(1) 

1 

(2) 

9.7 

„= 
*j! 

(3) 

9.5 

13 

o. 

<J 

1 

(5) 

• 
a 

3 

jj 

"3 

I-S 

9 

<3 

1 

1 

> 

i 

Q 

2 

(4) 

(6) 

(7) 

(8) 

(9) 

(10) 

(ii) 

(12) 

(13) 

9.4% 

9.1 

10.1 

10.2 

13.3 

9.3 

8.7 

8.8 

8.8 

9.0 

9.1 

Here  the  highest  per  cent  was  found  in  June.  These  figures 
are  influenced,  of  course,  by  the  numbers  of  deaths  from 
causes  other  than  tuberculosis. 


CHRONOLOGICAL  STUDY  OF  TUBERCULOSIS     317 

Chronological  study  of  tuberculosis.  —  The  death-rate 
from  tuberculosis  has  decreased  steadily  during  the  last 
generation  in  Massachusetts  as  shown  by  Fig.  50.  This 
curve  does  not  tell  us  many  of  the  things  which  we  desire  to 


JSO 


300 


250 


200 


/SO 


/oo 


V\ 


Desfh 


\ 


f/Of? 


/setts 


9/4 


FIG.  50.  —  Death-rates  from  Tuberculosis,  Massachusetts,  1873-1914. 

know.  It  shows  that  prior  to  1885  the  death-rate  exceeded 
300  per  100,000  but  that  now  it  is  in  the  vicinity  of  100.  It 
is  not  decreasing  arithmetically,  however.  Tuberculosis  will 
not  disappear  by  1940,  or  thereabouts  as  one  might  think  by 
a  hasty  forward  projection  of  the  plotted  line.  The  curve  is 


318 


STATISTICS  OF  PARTICULAR  DISEASES 


losing  slope.  Even  if  the  rate  of  decrease  remained  the  same 
from  year  to  year,  it  would  take  many,  many  years  for  the 
curve  to  reach  the  zero  iine. 

The  curve  does  not  tell  us  whether  it  is  the  lives  of  the 
young  or  the  old  which  are  being  saved.  It  is  not  easy  to 
obtain  specific  death-rates  for  tuberculosis  by  sex  and  age- 
groups  which  cover  a  long  period  of  years.  Even  if  we  had 
the  figures  they  would  not  be  very  reliable  because  of  changes 
which  are  being  made  in  the  diagnosis  of  the  disease. 

Tuberculosis  and  occupation.  —  Many  misleading  statis- 
tics relating  to  tuberculosis  and  occupation  are  continually 
being  published.  As  statements  of  facts  they  may  be 
correct,  but  they  are  often  subject  to  the  fallacy  of  concealed 
classification  and  therefore  give  false  impressions. 
1  A  recent  report  of  the  New  Jersey  State  Department  of 
Health  gives  statistics  of  deaths  from  tuberculosis  in  1916 
classified  by  age  and  occupation.  This  is  a  better  arrange- 
ment than  is  sometimes  used,  but  even  in  studying  these 
figures,  it  is  necessary  to  be  on  guard  against  wrong  con- 
clusions because  of  inadequate  data.  Thus  we  find  the 
following: 

TABLE    84 

DEATHS  FROM  TUBERCULOSIS  CLASSIFIED  BY  AGE  AND 
OCCUPATION:    NEW  JERSEY,  1916 


Ag 

e. 

Total 

10-19 

20-29 

30-39 

4(M9 

50-59 

60-69 

70^79 

80-89 

90+ 

(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

(7) 

(8) 

(9) 

(10) 

(11) 

Farmers  
Farm  laborers  
Clerks  
Housekeepers       and 
stewards   .... 

47 
11 
110 

858 

2 

2 
11 

34 

6 
2 
45 

276 

1 

3 

31 

?69 

9 
1 
20 

158 

11 

2 
2 

65 

9 

1 
1 

36 

6 
0 
0 

18 

3 
0 
0 

1 

0 
0 
0 

1 

General  laborers  
Stone  cutters  

364 
19 

12 
0 

61 
0 

96 
2 

115 
4 

49 

7 

27 
5 

4 
1 

0 

0 

0 
0 

TUBERCULOSIS  DEATH-RATE         319 

Why  is  the  number  of  deaths  from  tuberculosis  so  high 
among  housekeepers?  Not  because  housekeeping  imposes 
a  special  hazard,  but  because  there  are  so  many  housekeepers 
in  the  state.  Obviously  what  is  needed  here  are  the  specific 
rates  for  this  particular  disease  by  age-groups.  But  to 
compute  them  it  is  necessary  to  know  how  many  housekeepers 
there  are  in  the  state  in  each  age-group,  and  who  knows  these 
facts?  Also  are  the  ' '  stewards ' '  referred  to  male  or  female  ? 

Why  is  the  number  of  deaths  among  stone  cutters  so 
small?  This  occupation  is  certainly  hazardous  from  the 
standpoint  of  tuberculosis,  as  the  fine,  sharp,  stone  dust 
tends  to  lacerate  the  lungs.  We  cannot  draw  any  reliable 
conclusion  from  the  figures  because  we  do  not  know  how 
many  stone  cutters  there  are  in  each  group. 

We  notice  that  the  largest  number  of  deaths  from  tuber- 
culosis among  farmers  occurred  in  age-group  50-59,  but  that 
among  farm  laborers  in  age-group  30-39.  What  is^a  farmer 
and  what  is  a  farm  laborer?  We  must  know  that.  Also  do 
farm  laborers  ultimately  bec9me  farmers?  Is  there  a  shift- 
ing of  individuals  from  one  class  to  the  other  as  they  grow 
older? 

So  also  in  the  case  of  clerks.  The  largest  number  of 
deaths  is  in  age-group  20-29.  Do  the  clerks  die  off  at  this 
early  age  or  do  they  cease  to  be  clerks  ?  Are  the  clerks  male 
or  female  ? 

The  student  of  statistics  must  persistently  cultivate  this 
critical  faculty  until  it  becomes  a  habit.  It  may/esult  in  a 
cynical  and  pessimistic  frame  of  mind  in  regard  to  published 
vital  statistics,  but  even  this  is  better  than  an  easy  lapse  into 
an  unthinking  acceptance  of  all  statistics  at  their  face  value. 
Statistics  should  be  used  with  truth  or  they  had  better  not 
be  used  at  all. 

Racial  composition  of  population  and  tuberculosis  death- 
rate.  —  The  following  interesting  and  at  first  puzzling 


320 


STATISTICS  OF  PARTICULAR  DISEASES 


situation  will  serve  to  emphasize  the  importance  of  the 
careful  analysis  of  death-rates  and  the  necessity  of  taking 
into  account  not  only  specific  death-rates  but  the  composi- 
tion of  the  population. 

In  1910  the  death-rate  from  tuberculosis  of  the  lungs  was 
226  per  100,000  in  Richmond,  Va.,  and  187  in  New  York 
City,  and  yet  the  specific  death-rates  from  this  disease  for 
both  white  and  colored  persons  were  greater  in  New  York 
than  in  Richmond.  The  following  figures  were  taken  from 
the  U.  S.  Census  reports. 

TABLE    85 

TUBERCULOSIS  DEATH-RATES  IN   NEW  YORK  AND 
RICHMOND 


-  Class. 

Population. 

Number  of  deaths. 

Death-rate  per 
100,000. 

New 
York. 

Rich- 
mond. 

New 

York. 

Rich- 
mond. 

New 
York. 

Rich- 
mond. 

(1) 

(2) 

.(3) 

(4) 

(5) 

(6) 

(7) 

White  
Colored  
Total  

4,675,174 
91,709 
4,766,883 

80,895 
46,733 
127,628 

8368 
513 

8881 

131 
155 

286 

179 
560 

187 

162 
332 
226 

The  explanation  of  this  anomaly  lies,  of  course,  in  the  fact 
that  in  Richmond  more  than  one-third  of  the  population  is 
colored,  while  in  New  York  the  colored  population  is  less 
than  two  per  cent. 

Many  similar  comparisons  can  be  found  between  northern 
and  southern  cities.  This  is  merely  a  striking  case. 

Diphtheria  in  Cambridge,  Mass.  —  Applying  the  same 
methods  to  the  study  of  diphtheria  we  have  the  following 
figures: 


DIPHTHERIA  IN   CAMBRIDGE,   MASS. 


321 


TABLE  86 

CAMBRIDGE,  MASS.,  1916 
Statistics  of  Diphtheria,  Cases  and  Deaths  Arranged  by  Age  and  Sex 


Age- 

Population. 

Deaths,  all 
causes. 

Deaths  from 
diphtheria. 

Cases  of 
diphtheria. 

Male. 

Female. 

Male. 

Female. 

Male. 

Female. 

Male. 

Female. 

_  W 

(2) 

(3) 

(4) 

(5) 

(6) 

(7) 

(8) 

(9) 

0-1 

1,114 

1,080 

138 

105 

1 

3 

7 

4 

1-4 

4,161 

4,120 

38 

40 

4 

6 

56 

67 

5-9 

4,996 

5,000 

13 

13 

5 

5 

63 

80 

10-14 

4,488 

4,533 

7 

6 

1 

1 

15 

24 

15-19 

4,569 

4,901 

22 

12 

1 

0 

7 

4 

20-29 

10,424 

11,326 

44 

51 

1 

0 

8 

12 

30-39 

8,334 

9,190 

64 

43 

0 

0 

4 

5 

40H19 

6,552 

7,177 

80 

76 

0 

0 

0 

1 

50-59 

4,133 

4,823 

88 

85 

0 

0 

0 

1 

60- 

3,224 

4,678 

229 

306 

0 

0 

0 

0 

Total 

51,995 

56,808 

723 

737 

13 

15 

160 

198 

Age- 
group. 

Morbidity 
(case;  rate 
per  10,000. 

Percentage 
distribution 
of  cases. 

Mortality 
(death) 
rate. 

Percentage 
distribution 
of  deaths. 

Proportion- 
ate mortal- 
ity ,per  cent. 

Fatality, 
per  cent. 

J2 

"3 

£ 

"c8 

Q 
| 

4 

_o 

"3 

s 

& 

.£ 

• 

£ 

1 

£ 

JS 

£ 

d 

i 

J2 

1 

1 

£ 

£ 

(1) 

(10) 

(11) 

(12) 

(13) 

(14) 

(15) 

(16) 

(17) 

(18) 

(19) 

2.8 
15.0 
38.4 
16.7 
0.0 
0.0 
0.0 
0.0 
0.0 
0.0 
2.0 

(20) 

14 

7 
8 
7 
14 
13 
0 
0 
0 
0 
8 

(21) 

75 

9 
6 
4 
0 
0 
0 
0 
0 
0 
7 

0-1 
1-4 
5-9 
10-14 
15-19 
20-29 
30-39 
40-49 
50-59 
60- 
Total 

629 
1340 
1262 
334 
153 
76 
48 
0 
0 
0 

371 
1630 
1600 
528 
82 
106 
55 
14 
21 
0 
349 

4.4 
3  .0 
39.3 
9.4 
4.4 
5.0 
2.5 
0.0 
0.0 
0.0 

2.0 
33.9 
40.4 
12.1 
2.0 
6.1 
2.5 
0.5 
0.5 
0.0 

90 
96 
100 
22 
22 
9 
0 
0 
0 
0 

278 
146 
100 
22 
0 
0 
0 
0 
-  0 
0 

7.7 
30.7 
38.5 
7.7 
7.7 
7.7 
0.0 
0.0 
0.0 
0.0 

20.0 
40.0 
33.3 
6.7 
0.0 
0.0 
0.0 
0.0 
0.0 
0.0 

0.7 
10.5 
38.4 
14.3 
4.5 
2.2 
0.0 
0.0 
0.0 
0.0 

308 

100.0 

100.0 

25 

26 

100.0 

100.0 

1.8 

322 


STATISTICS  OF  PARTICULAR  DISEASES 


Here  we  see  that  the  maximum  age  incidence  occurs  be- 
tween the  ages  of  one  and  ten  for  both  males  and  females. 
The  morbidity  rate  in  Cambridge  for  this  year  was  higher 
for  females  than  for  males,  but  the  percentage  distribution 
of  the  cases  was  about  the  same  for  the  two  sexes.  The 
mortality  rates  followed  the  morbidity  rates  rather  closely, 
and  the  fatality  was  fairly  constant  except  for  infant  females. 
The  proportionate  mortality  was  highest  in  age-group  5-9. 
It  must  be  remembered  that  these  rates  are  computed  from 
small  numbers  of  cases  and  deaths,  hence  no  very  uniform 
or  significant  conclusions  can  be  drawn  from  them.  It  is 
only  by  using  large  numbers  of  events  that  significant 
tendencies  can  be  shown.  The  differences  between  the 
occurrence  of  diphtheria  and  tuberculosis  are,  however,  very 
striking. 

The  seasonal  distribution  of  reported  cases  of  diphtheria 
was  as  follows: 

TABLE  87 

SEASONAL  DISTRIBUTION  OF  DIPHTHERIA  CASES: 
CAMBRIDGE,  MASS.,   1916 


1 

J2 

£ 

1 

1*T 

! 

1 

1 

j*. 

"3 

^ 

3 

<5 

! 

t 

(ID 

g 

i 

I 

(1) 

(2) 

(3) 

(5) 

(6) 

(7) 

(8) 

(9) 

(10) 

(12) 

38 

(13) 

(14) 

Number  of  cases  .... 

24 

35 

37 

44 

31 

32 

21 

15 

20 

25 

36 

358 

It  will  be  noticed  that  the  lowest'  numbers  were  reported 
during  the  summer  vacation  months. 

Knowing  that  the  incidence  of  the  disease  was  greatest 
during  the  school  ages  does  this  indicate  that  schools  played 
an  important  part  in  spreading  the  infection  ?  Do  these 
statistics  prom  it?  If  not,  what  other  statistics  would  be 
necessary  to  prove  it? 


AGE  SUSCEPTIBILITY  TO   DIPHTHERIA 


323 


Age  susceptibility  to  diphtheria.  —  Dr.  Charles  V.  Chapin 
the  Superintendent  of  Health,  of  Providence,  R.  I.,  has  been 
in  the  habit  of  computing  what  he  calls  the  attack  rate.  This 
is  a  ratio  between  the  number  of  cases  and  the  number  of 
persons  exposed,  that  is,  all  the  members  of  the  family  where 
the  disease  occurred,  including  the  cases  and  those  who  were 
removed  from  home  after  the  disease  developed.  The  follow- 
ing figures,  given  in  Dr.  Chapin's  report  for  the  year  1915, 
are  based  on  a  study  of  53,280  exposed  persons  during  1889- 
1915. 

TABLE  88 
DIPHTHERIA  ATTACK  RATE:    PROVIDENCE,  R.  I.,  1915 


Age-group. 

Attack  rate 
(per  cent). 

Age-group. 

Attack  rate 
(per  cent). 

(1) 

(2) 

(1) 

(2) 

0-1  yr. 

16.70 

12+  yr. 

31.12 

1+ 

43.65 

13+ 

26.08 

2+ 

54.55 

14+ 

22.41 

3+ 

55.61 

15+ 

18.92 

4+ 

55.91 

16+ 

18.58 

5+ 

53.99 

17+ 

17.85 

6+ 

53.82 

18+ 

16.86 

7+ 

49.33 

19+ 

17.33 

8+ 

44.31 

20+ 

23.56 

9+ 

40.91 

Adults 

6.83 

10+, 

36.42. 

Total 

25.45 

11+ 

35.35 

These  figures  indicate  that  the  chance  of  exposed  persons 
acquiring  the  disease  in"  recognizable  form  is  highest  at  age 
four  and  decreases  steadily  as  the  age  increases.  At  the 
most  susceptible  period  more  than  half  of  those  exposed 
came  down  with  diphtheria. 

It  was  found  that  between  the  years  1889  and  1915  out  of 
6822  families  who  lived  in  houses  where  the  disease  existed 
in  other  families,  only  474  of  these  exposed  families  were 


324 


STATISTICS  OF  PARTICULAR  DISEASES 


attacked.  This  is  only  6.9  per  cent.  In  most  of  these  cases 
of  attacked  families  there  had  been  some  sort  of  intercourse 
with  the  infected  families,  that  is  enough  to  transmit  the 
disease  by  contact. 

Fatality  of  diphtheria.  —  Dr.  Chapin  has  also  kept  a 
careful  record  of  the  fatality  of  diphtheria  in  Providence. 
In  1884  it  was  30  per  cent,  and  a  few  years  later  it  rose  to 
42  per  cent.  Between  1895  and  1896  it  dropped  from  20 
per  cent  to  14  per  cent,  since  which  date  it  has  fallen  until 
now  it  is  only  about  8  per  cent,  that  is,  there  is  only  one  death 
for  each  12  cases.  The  fatality  is  not  the  same  at  all  ages  as 
the  following  table  l  shows : 


TABLE  89 
DIPHTHERIA  CASE  FATALITY  AT  DIFFERENT  AGES 


A  no. 

1889-1914. 

1915. 

Age. 

Cases. 

Deaths. 

Fatality. 

Cases. 

Deaths. 

Fatality. 

(1) 

(2) 

(3) 

(4) 

(5) 

(8) 

(7) 

0-1 

280 

96 

34.28 

21 

2 

9.52 

1+ 

706 

247 

34.99 

43 

6 

13.95 

2-4 

3,322 

697 

20.98 

181 

24 

13.26 

5-9 

4,541 

460 

10.13 

219 

15 

6.85 

10-14 

1,801 

83 

4.61 

9 

3 

3.79 

15-19 

616 

26 

4.22 

20 

1 

5.00 

20+ 

1.670 

40 

2.39 

62 

2 

3.23 

Total 

12,936 

1649 

12.74 

625 

53 

8.48 

The  greatest  decrease  in  the  fatality  of  the  disease  has 
occurred  among  young  children. 

To  a  large  extent  the  decreased  fatality  has  been  due  to 
the  use  of  antitoxin,  which  decreased  the  number  of  deaths. 
To  some  extent  it  may  have  been  due  to  better  diagnosis  by 

1  Ann.  Report  Providence  Supt.  of  Health,  1915,  p.  64. 


URBAN  AND  RURAL  DISTRIBUTION  OF  DIPHTHERIA   325 

culture.  If  this  practice  increased  the  number  of  recognized 
cases  it  would  decrease  the  fatality  rates. 

Diphtheria  is  a  short  disease.  Hence  the  fatality  can  be 
computed  far  more  accurately  than  in  the  case  of  tubercu- 
losis. 

Chronological  study  of  diphtheria.  —  Fig.  51 l  shows 
the  decrease  in  the  death-rate  from  diphtheria  in  Massa- 
chusetts since  1873.  In  1876  the  rate  was  very  high,  about 
195  per  100,000.  It  has  decreased  very  greatly  until  now  it 
is  usually  less  than  20  per  100,000.  Recurrences  of  diph- 
theria have  occurred  at  intervals  of  five  or  six  years.  After 
the  great  epidemic  of  1876  there  was  no  important  recurrence 
until  1889,  but  after  that  recurrences  were  noted  in  1894  and 
1900.  Since  then,  thanks  no  doubt  to  preventive  medicine, 
the  recurrences  have  been  so  slight  as  to  be  almost  un- 
noticed. 

What  is  the  reason  for  these  recurrences,  for  this  periodic 
development  of  diphtheria?  In  a  general  way,  whooping 
cough,  scarlet  fever,  measles,  all  children's  diseases,  have 
similar  recurrences.  It  is  commonly  explained  on  the  theory 
of  susceptibility.  It  has  already  been  seen  that  the  rate  of 
attack  of  exposed  persons  is  very  high  among  young  children. 
It  is  known,  too,  that  one  attack  usually  makes  .the  victim 
relatively  immune  against  a  second  attack.  After  a  period 
of  relative  quiescence  during  which  the  class  of  susceptible 
children  has  been  annually  recruited  it  is  natural  to  expect 
that  an  epidemic  may  spread.  This  is  apparently  what 
happened  until  the  methods  of  preventive  medicine  came 
to  be  generally  used.  It  probably  still  happens,  but  to  a 
less  extent  than  formerly. 

Urban  and  rural  distribution  of  diphtheria.  —  It  is  not 
easy  to  obtain  complete  statements  of  the  facts  to  show  the 
differences  between  the  occurrence  of  diphtheria  in  cities  and 
1  State  Sanitation,  Vol.  I,  p.  167. 


326 


STATISTICS  OF   PARTICULAR  DISEASES 


/87S         /880 

FIG.  51.  —  Death-rates 


/S9O       /89S       /9OO 
ye&r*. 

from  Diphtheria,  Massachusetts,  1873-1914. 


STATISTICAL  STUDY  OF  TYPHOID  FEVER        327 


rural  districts.  Occasionally  partial  statements  are  pub- 
lished. In  the  annual  report  of  the  Michigan  State  Board 
of  Health  for  1916-17  it  is  stated  that  for  the  period  1904-15 
the  morbidity  rate  was  213  per  100,000  in  urban  districts  and 
82  in  rural  districts;  the  mortality  rates  for  1908-1915  were 
16.2  and  12.2  per  100,000  respectively.  The  fatality  was 
10.9  per  cent  for  cities  and  15.7  for  urban  districts.  No 
separations  were  made  according  to  age  and  sex  and  it  is 
difficult  to  find  these  facts.  There  is,  however,  quite  a 
difference  in  the  age  distribution  of  diphtheria  between  the 
city  and  the  country.  In  general  the  average  age  of  diph- 
theria cases,  as  well  as  of  persons  dying  from  this  disease,  is 
lower  in  4the  city.  The  following  facts  were  taken  almost 
at  random  from  the  Mortality  Statistics  of  1914: 

TABLE  90 

PERCENTAGE  AGE  DISTRIBUTION  OF  DEATHS  FROM 
DIPHTHERIA 


A  __ 

Cities. 

Rural  states. 

Age. 

New  York. 

Boston. 

Vermont. 

New 

Hampshire. 

Maine. 

(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

0+ 

10.7 

7.7 

0.0 

6.7 

9.3 

1+ 

25.9 

21.4 

5.2 

17.8 

10.5 

2+ 

16.5 

13.7 

18.4 

11.1 

16.3 

3+ 

13.7 

14.9 

18.4 

8.9 

9.3 

4+ 

9.7 

6.0 

13:1 

17.8 

7.0 

5-9    (per  year) 

3.7 

5.3 

6.3 

4.0 

7.0 

.  10-19     .    " 

0.26 

0.6 

0.52 

1.55 

0.7 

20-29 

0.14 

0.12 

0.0 

0.0 

0.23 

30-39 

0.05 

0.06 

0.0 

0.0 

0.23 

Statistical  study  of  typhoid  fever.  —  Typhoid  fever  has 
been  given  a  great  deal  of  attention  from  the  statistical 
point  of  view.  Hundreds  of  scientific  papers  describing 


328  STATISTICS  OF  PARTICULAR  DISEASES 

local  outbreaks  of  the  disease,  variations  in  the  typhoid  fever 
death-rate  and  so  on  have  been  published.  For  the  most 
part  these  have  been  extensive  and  not  intensive  studies. 
It  is  rather  surprising,  when  we  view  this  enormous  mass  of 
statistics,  how  little  we  know  about  certain  important  points, 
such  as  the  morbidity  and  fatality  rates  at  different  ages. 
Our  interest  has  been  engrossed  by  the  more  important 
matter  of  causation.  There  are  many  ways  in  which  the 
disease  may  be  communicated  from  one  person  to  another 
and  this  question  must  be  answered  for  each  particular  out- 
break or  epidemic.  The  interest  in  statistical  studies  of 
typhoid  fever  has,  therefore,  centered  around  the  subject  of 
correlation,  a  phase  of  statistics  which  we  shall  consider  in 
Chapter  XIII.  It  will  be  useful  to  consider  at  this  point 
some  of  the  fundamental  relations  of  this  disease  to  human 
beings.  Those  who  are  interested  in  the  epidemiology  of 
the  subject  are  referred  to  the  author's  book  on  Typhoid 
Fever.  This  book,  it  should  be  said,  is  to-day  somewhat 
out  of  date,  although  its  historical  value  remains. 

Age  distribution  of  typhoid  fever.  —  The  largest  number 
of  deaths  from  typhoid  fever  is  generally  found  in  age-group 
20-29  years.  Table  91  shows  the  percentage  distribution  of 
deaths  by  ages  according  to  the  U.  S.  Census  1  for  1900. 

In  the  case  of  epidemics  caused  by  a  widely  scattered  in- 
fection, as  through  the  public  water-supply,  the  age  dis- 
tribution of  the  deaths  usually  approximates  these  figures. 
If,  however,  the  outbreak  occurs  in  a  school-house  or  is 
caused  by  infected  milk,  which  is  used  more  freely  by  children 
than  by  adults,  the  larger  numbers  of  deaths  may  occur  in 
the  lower  ages;  in  fact,  this  is  a  test  often  applied  in  the  study 
of  typhoid  fever  outbreaks. 

1  Vital  Statistics,  Vol.  Ill,  Part  I,  page  cxlyi. 


AGE  DISTRIBUTION  OF  TYPHOID  FEVER         329 


TABLE  91 

PERCENTAGE  DISTRIBUTION   OF  DEATHS  FROM 
TYPHOID   FEVER;   UNITED   STATES:    1900 


Age-group. 

Per  cent  of  deaths. 

Age-group. 

Per  cent  of  deaths. 

(1) 

(2) 

(1) 

(2) 

0-4 

4.09 

50-54 

3.52 

5-9 

5.05 

55-59 

2.55 

10-14 

5.20 

60-64 

1.95 

15-19 

11.23 

65-69 

1.12 

20-24 

17.78 

70-74 

0.91 

25-29 

15.09 

75-79 

0.34 

30-34 

11.46 

80-84 

0.11 

35-39 

9.12 

85-89 

0.09 

40-44 

5.77 

Total 

100.00 

45-49 

4.62 

If  we  take  the  specific  death-rates  by  sex  and  ages  we 
obtain  the  following  figures: 

TABLE  92 

SPECIFIC  DEATH-RATES  FOR  TYPHOID   FEVER 
United  States:  1900 


Rate  per  100,000. 

Rate  per  100,000. 

Age-group. 

Age-group. 

Males. 

Females. 

Males. 

Females. 

(1) 

'(2) 

(3) 

(1) 

(2) 

(3) 

0-4 

12 

16 

45-49 

34 

29 

5-9 

15 

21 

50-54 

30 

30 

10-14 

17 

31 

55-59 

30 

33 

15-19 

45 

53 

60-64 

29 

33 

20-24 

66 

57 

65-69 

22 

40 

25-29 

61 

48 

70-74 

'    27  ' 

43 

30-34 

53 

43 

75-79 

20 

23 

35-39 

48 

39 

80-84 

10 

26 

40-44 

34 

37 

85-89 

16 

35 

330 


STATISTICS  OF  PARTICULAR  DISEASES 


It  will  be  noticed  that  these  differences  are  not  as  great 
as  in  the  previous  table.  This  is  because  there  are  fewer 
persons  living  at  the  ages  above  50  and  even  if  the  specific 
rate  remained  high  there  would  not  be  as  many  deaths.  It 
is  for  this  reason  that  both  the  age  distribution  of  deaths 
and  the  specific  death-rate  are  important  tabulations.  The 
specific  rates  just  given  represent  practical  conditions  and 
take  into  account  the  important  element  of  exposure.  The 
difference  between  the  death-rates  of  males  and  females  at 
ages  25-29  must  not  be  regarded  as  having  a  physiological 
basis,  for  at  those  ages  males  are  more  exposed  to  the  dis- 
ease than  females. 

Except  at  times  of  epidemics  typhoid  fever  is  not  a  well- 
reported  disease.  It  is  difficult  therefore  to  obtain  reliable 
specific  morbidity  rates  by  sex  and  ages.  Such  as  have  been 
computed,  however,  show  an  age  distribution  very  similar  to 
that  of  deaths,  but  with  a  tendency  towards  larger  per- 
centages of  cases  in  the  earlier  years. 

The  fatality  of  the  disease  at  different  ages  is  not  as  well- 
established  as  it  ought  to  be.  Computations  by  the  author, 
by  Newsholme,  by  A.  W.  Freeman,1  seem  to  warrant  the 
following  approximate  figures: 

TABLE  93 
APPROXIMATE   CASE  FATALITY  IN   TYPHOID   FEVER 


Age. 

Per  cent. 

Age. 

Per  cent. 

(1) 

(?) 

(1) 

(2) 

0 

15 

40 

21 

10 

8 

50 

25 

20 

15 

60 

42 

30 

18 

All  ages 

14 

1  Case  Fatality  in  Typhoid  Fever,  Public  Health  Reports,  Dec.  8, 
1916. 


SEASONAL  DISTRIBUTION  OF  TYPHOID  FEVER     331 


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FIG.  52.  —  Diagram  Showing  the  Relation  between  Atmospheric  Tem- 
perature and  Seasonal  Distribution  of  Typhoid  Fever.  (After  Sedg- 
wick  and  Winslow.) 


332  STATISTICS  OF  PARTICULAR  DISEASES 

It  is  probable,  therefore,  that  there  is  much  unreported 
typhoid  fever  among  children,  some  of  it  doubtless  unrecog- 
nized. 

Seasonal  distribution  of  typhoid  fever.  —  The  seasonal 
distribution  of  typhoid  fever  appears  to  be  closely  related  to 
the  manner  in  which  the  infection  is  communicated.  Nor- 
mally there  appears  to  be  a  fairly  close  relation  between 
typhoid  death-rates  and  atmospheric  temperature,  as  shown 
in  Fig.  52.  Water-borne  typhoid  is  most  common  during 
the  colder  months  of  the  year.  Examples  of  seasonal  dis- 
tribution of  typhoid  fever  are  to  be  found  in  many  epidemio- 
logical  studies. 

Chronological  reduction  in  typhoid  fever.  — The  reduc- 
tion in  the  amount  of  typhoid  fever  in  the  United  States 
during  the  last  twenty-five  years  has  been  general  and  steady. 
From  being  one  of  our  most  dreaded  diseases  it  seems  likely 
to  almost  disappear.  This  has  been  due  to  many  things. 
George  A.  Johnson,1  in  an  exhaustive  compilation  of  statistics, 
gives  the  chief  credit  to  the  purification  of  public  water 
supplies  by  filtration,  his  conclusions  being  summed  up  in 
Fig.  53.  His  main  contention  is  doubtless  correct,  but  the 
purification  of  water  is  only  one  of  many  factors  in  the  prob- 
lem. The  safeguards  thrown  around  milk  and  other  foods, 
the  better  understanding  of  the  idea  of  contact,  the  con- 
stantly decreasing  number  of  typhoid  carriers  since  the  Civil 
War  and  since  the  purification  of  water-supplies,  the  recent 
extensive  use  of  vaccination  methods,  have  contributed  to 
the  present  low  and  falling  death-rates.  The  typhoid-fever 
death-rates  in  many  cities  using  unfiltered  water-supplies 
have  fallen  along  with  the  others.  This,  however,  is  no  argu- 
ment against  the  need  of  water  purification.  It  does  show 
the  need  of  very  careful  analysis  of  the  data.  Extensive 
studies,  like  those  of  Johnson,  have  their  value,  but  they  are 
1  The  Typhoid  Toll,  Jour.  Am.  Water  Works  Assoc.,  June,  1916. 


CHRONOLOGICAL  REDUCTION  IN  TYPHOID  FEVER  333 


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FIG.  53.  —  Relation  between  Typhoid  Fever  and  Water  Filtration. 
After  Johnson. 


334  STATISTICS  OF  PARTICULAR  DISEASES 

not  to  be  compared  in  importance  with  more  fully  analyzed 
and  more  critical  statistical  studies. 

Statistics  of  cancer.  —  Let  us  now  take  up  a  disease  which 
is  quite  different  from  tuberculosis,  diphtheria  and  typhoid 
fever,  namely,  cancer.  This  involves  some  interesting  appli- 
cations of  statistical  principles.  The  subject  is  one  which 
demands  most  careful  investigation  and  the  reader  should 
by  all  means  read  a  paper  on  "The  Alleged  Increase  of 
Cancer/'  by  Prof.  Walter  F.  Willcox,  of  Cornell  University, 
as  a  splendid  example  of  critical  work.1 

Extensive  studies  of  death-rates  have  shown  that  as  a 
reported  cause  of  death  cancer  is  on  the  increase.  Dr.  F.  L. 
Hoffman  in  a  most  elaborate  monograph  entitled  "The 
Mortality  of  Cancer  throughout  the  World,"  2  has  demon- 
strated this  fact.  But  is  this  reported  increase  an  actual 
increase  ?  Is  it  due  to  changing  conceptions  of  the  statistical 
unit,  to  a  better  recognition  of  the  disease,  to  differences  in 
the  composition  of  populations?  Messrs.  King  and  News- 
holme,3  take  the  ground  that  the  alleged  increase  is  due  to 
statistical  fallacies.  Their  conclusion  is  based  on  intensive 
studies.  Willcox,  in  the  article  referred  to,  has  made  a  critical 
comparison  of  these  two  points  of  view,  and  his  conclusions 
are  that  "improvements  in  diagnosis  and  changes  in  age 
composition  explain  away  more  than  half  and  perhaps  all  of 
apparent  increase  in  cancer  mortality." 

It  is  admitted  at  the  start  that  no  reliable  statistics  of 
cancer  morbidity  exist.  Therefore,  neither  morbidity  nor 
fatality  rates  can  be  computed.  The  entire  discussion  rests 
on  deaths. 

The  increase  in  reported  deaths  from  cancer  is  well  shown 
by  the  following  figures: 

1  Quar.  Pub.  Am.  Sta.  Asso.,  Sept.  1917,  Vol.  XV,  p.  701. 

2  Published  in  1915,  by  the  Prudential  Press,  Newark,  N.  J. 

3  Proc.  Royal  Society,  1893,  liv,  pp.  209-242. 


STATISTICS  OF  CANCER 


335 


TABLE  94 

DEATH-RATES  FROM   CANCER 
U.  S.  Registration  Area  of  1900 


Rate  per  100,000. 

Year 

Male. 

Female. 

(1) 

(2) 

(3) 

1900 

47.0 

80.7 

1905 

53.0 

92.1 

1910 

62.6 

103  .7 

1915 

72.3 

111.9 

The  death-rate  for  females  is  considerably  higher  than  for 
males. 
The  specific  death-rate  by  ages  and  sex  runs  as  follows: 

TABLE  95 

SPECIFIC   DEATH-RATES  FOR  CANCER 
U.  S.  Registration  Area  of  1900  for  the  Year  1910 


Rate  per  100,000. 

Rate  per  100,000. 

Age-group. 

Age-group. 

^ 

Male. 

Female. 

Male. 

Female. 

(1) 

(2) 

(3) 

(1) 

(2) 

(3) 

0-5 

4.1 

2.8 

35-44 

33.0 

88.9 

5-9 

1.5 

1.2 

45-54 

106.7 

230.7 

10-14 

1.8 

1.4 

55-64 

272.0 

411.3 

15-19 

2.9 

3.5 

65^-74 

493.6 

616.2 

20-24 

4.9            4.1 

75- 

693.7 

867.8 

25-34 

9.5 

21.9 

By  applying  the  method  of  adjustment  to  the  Standard 
Million  of  Population,  Willcox  finds  that  for  England  and 
Wales  in  1911  the  death-rate  from  cancer  should  have  been 


336  STATISTICS  OF  PARTICULAR  DISEASES 

91.5  instead  of  99.3  per  100,000.  In  1901  it  was  84.3;  hence 
the  increase  would  have  been  8.7  per  cent,  instead  of  17.8 
per  cent,  if  computed  on  the  basis  of  similar  populations. 
Similar  comparisons  are  made  for  other  populations,  from  all 
of  which  the  conclusion  is  drawn  that  about  one-third  of  the 
increase  in  all  the  populations  considered  is  due  to  changes 
in  sex  and  age  composition. 

In  regard  to  diagnosis  many  interesting  facts  are  presented. 
There  are  differences  between  the  statistics  for  accessible  and 
inaccessible  cancer,  the  increase  being  chiefly  in  the  latter. 
" Laymen  seldom  report  cancer  as  a  cause  of  death,"  and 
there  appears  to  be  a  correlation  between  cancer  increase 
and  an  increase  in  the  number  of  physicians  per  100,000  of 
population,  and  the  number  of  medical  certificates  signed  by 
competent,  persons.  The  increase  in  hospitals  is  also  a 
factor.  Deaths  ascribed  to  tumor,  and  to  "old  age,"  have 
been  decreasing,  as  cancer  has  increased,  and  the  implication 
is  that  there  has  been  a  shifting  of  these  statistical  units. 
For  all  of  these  deaths  the  reader  should  consult  Willcox's 
paper.  He  gives  also,  by  way  of  analogy^  a  comparison 
between  cancer  and  appendicitis,  which  shows  that  the  rate 
of  increase  in  reported  causes  of  death  are  substantially  the 
same  for  the  two  diseases,  namely,  44  per  cent  and  40  per 
cent  respectively  between  1900  and  1915.  The  upshot  of 
this  investigation  is  that  there  is  no  more  reason  for  people 
to  fear  dying  from  cancer  now  than  there  was  a  generation 
ago.  The  disease  has  not  changed,  people  have  not  changed; 
it  is  the  reports  of  the  physicians  which  have  changed  because 
of  their  increased  knowledge.  Is  this  the  last  word  on  the 
subject?  Probably  not. 

Further  studies  of  particular  diseases.  —  It  is  not  possible 
to  take  up  the  hundred  or  more  particular  diseases  and 
discuss  them  by  means  of  statistics.  This,  however,  is  one 
of  the  chief  uses  of  vital  statistics.  Enough  has  been  given 


EXERCISES  AND  QUESTIONS  337 

perhaps  to  illustrate  the  method  of  procedure,  and  to  em- 
phasize the  impprtance  of  critical  statistical  analysis.  The 
necessity  of  considering  specific  rates,  and  varying  composi- 
tions of  populations  in  all  these  studies  cannot  be  too  strongly 
insisted  on. 

The  student  will  find  it  a  fascinating  and  highly  valuable 
study  to  take  up  some  disease  in  which  he  may  be  interested 
and  study  it  intensively.  There  is  room  in  statistical  litera- 
ture for  many  monographs  treating  of  the  statistics  of 
particular  diseases. 


EXERCISES   AND    QUESTIONS 

1.  Describe  the  cycles  of  whooping  cough  in  New  York  State  since 
1885.     [N.  Y.  State  Dept.  of  Health,  Monthly  Bulletin,  March  1917, 
p.  70.J 

2.  How  would  you  find  out  what  proportion  of  all  children  born  have 
whooping  cough  at  some  time  in  their  lives?     Try  to  make  up  a  table 
from  morbidity  statistics  of  whooping  cough  classified  by  age  in  years, 
and  see  if  you  cannot  determine  this.     Select,  for  example,  the  year 
1910.     How  many  babies  were  born  that  year  and  how  many  had  had 
whooping  cough  while  infants?     In  1911  how  many  cases  of  whooping 
cough  were  in  age-group  1-2;  in  1912  how  many  in  age-groups  2-3,  etc.? 
Add  these  together  and  compare  the  result  with  the  births  in  1910. 
Then  do  the  same  starting  with  1909,  and  then  1908,  etc.     Compare  all 
the  results.     Are  they  more  uniform  than  the  ordinary  annual  statistics 
for  whooping  cough? 

3.  Make  the  same  sort  of  study  for  measles. 

4.  Make  the  same  sort  of  study  for  diphtheria. 
6.    Make  the  same  sort  of  study  for  scarlet  fever. 

6.  Compare  death-rates  for  whooping  cough,  measles,  etc.,  in  urban 
and  rural  districts.     What  foundation  is  there  for  Farr's  law  that 
contagious  diseases  increase  as  the  density  of  population? 

7.  Explain  the  recent  finding  that  the  death-rates  from  measles  in 
the  U.  S.  army  cantonments  has  varied  inversely  as  the  density  of 
population  (percentage  of  urban  population)  in  the  states  from  which 
the  soldiers  came. 


338  STATISTICS  OF  PARTICULAR  DISEASES 

8.  Describe  the  periodicity  of  whooping  cough  in  Sweden.     (See 
Stephenson  and  Murray's  Textbook  of  Hygiene.) 

9.  Describe  the  age  distribution  of  Pellagra.     [See  Amer.  J.  P.  H., 
July/1918,  p.  488.] 

10.  What  reduction  in  diphtheria  has  occurred  as  a  result  of  the  use 
of  anti-toxin.     [See  Am.  J.  P.  H.,  May,  1917,  p.  445.] 

11.  Is  appendicitis  increasing?     [See  Am.  J.  P.  H.,  July,  1916.] 

12.  Make  a  statistical  summary  of  the  influenza  epidemic  of  1889-90. 
Consult  reports  of  state  and  city  departments  of  health. 

13.  Make  a  statistical  study  of  the  influenza  epidemic  of  1918  for 
some  state,  city  or  town. 

14.  Prepare  a  short  statistical  summary  of  cancer,  —  its  geographi- 
cal distribution,  its  occurrence  among  different   age-groups,  its  chro- 
nology, etc.     [Hoffman,  Frederick  L.     The  Mortality  from    Cancer 
throughout  the  World.    Newark.    The  Prudential  Press,  1915.] 


CHAPTER  XI 
STUDIES   OF   DEATHS   BY  AGE  PERIODS 

Infant  mortality.  —  No  part  of  vital  statistics  is  attracting 
more  attention  nowadays  than  the  subject  of  infant  mor- 
tality. It  is,  indeed,  a  serious  problem  and  worthy  of  most 
careful  study.  It  is  a  complex  problem  and  one  difficult  to 
understand.  It  is  a  problem  which  goes  beyond  itself. 
Newsholme  says  that  "infant  mortality  is  the  most  sensitive 
index  of  social  welfare  and  of  sanitary  improvements  which 
we  possess."  Another  says  that  "infant  mortality  is  to  the 
health  officer  what  the  clinical  thermometer  is  to  the  physi- 
cian." People  who  will  not  take  care  of  their  offspring  will 
not  take  care  of  themselves. 

Some  definitions.  —  The  term  infant  is  applied  to  any 
child  from  the  day  of  its  birth  up  to  one  year  of  age.  A  child 
born  dead  is  not  regarded  as  having  been  born.  It  is  not 
included  among  either  births  or  deaths;  it  is  a  still-birth. 
But  if  the  child  is  born  alive  and  dies  almost  immediately  it  is 
to  be  regarded  as  an  infant  and  both  its  birth  and  its  death 
is  to  be  recognized  statistically.  In  the  past  health  officials 
were  not  careful  to  make  this  distinction  and  many  of  the 
old  statistics  are  for  that  reason  not  comparable  with  present- 
day  records.  This  should  be  kept  in  mind  in  comparing 
statistics  which  extend  over  long  periods  of  time. 

The  specific  death-rate  for  infants,  that  is,  for  age-group 
0-1,  is  computed  in  the  same  way  as  the  specific  death-rate 
for  any  other  age-group,  namely,  by  dividing  the  annual 
number  of  deaths  in  the  group  by  the  mid -year  population  of 

339 


340 


STUDIES  OF  DEATHS  BY  AGE  PERIODS 


the  group,  expressed  in  thousands.  By  infant  mortality,  as 
the  term  is  generally  understood,  is  meant  something  slightly 
different,  namely,  the  number  of  infant  deaths  in  a  calendar 
year  divided  by  the  number  of  births  during  the  same  year. 

Prenatal  deaths.  —  Foetal  deaths  which  occur  before  the 
sixth  or  seventh  month  of  gestation  are  known  as  miscarriages 
and  are  not  reportable  or  recognized  in  ordinary  statistical 
work;  those  which  occur  later  than  this  are  called  still- 
births and  must  be  reported.  The  time  limit  is  sometimes 
stated  as  twenty-eight  weeks,  sometimes  it  is  made  dependent 
upon  the  apparent  condition  of  the  foetus.  Still-births, 
although  reportable,  should  always  be  kept  apart  from  true 
births. 

The  following  figures  show  how  in  Boston  the  ratio  of  still- 
births to  total  population  and  the  ratio  between  still-births 
and  living. births  have  changed  during  the  last  twenty  years. 


TABLE  96 
STILL-BIRTHS,  BOSTON 


Year. 

Number  per 
100  living 

Number  per 
1000  inhabi- 

Year. 

Number  per 
100  living 

Number  per 
1000  inhabi- 

births. 

tants. 

births. 

tants. 

(1) 

(2) 

(3) 

(1) 

(2) 

(3) 

1891 

4.2 

.3 

1904 

4.0 

1.1 

1892 

4.2 

.2 

1905 

4.2 

1.1 

1893 

4.1 

.3 

1906 

3.8 

1.1 

1894 

4.5 

.4 

1907 

4.0 

1.2 

1895 

3.8 

.2 

1908 

3.4 

1.0 

1896 

3.9 

.3 

1909 

4.0 

1.1 

1897 

3.6 

.2 

1910 

3.0 

1.0 

1898 

3.7 

.1 

1911 

1899 

3.3 

.0 

1912 

1900 

3.5 

.0 

1913 

1901 

3.6 

.0 

1914 

1902 

3.9 

1.1 

1915 

1903 

4.0 

1.1 

INFANT  MORTALITY  341 

The  monthly  records  show  no  appreciable  variation  in  the 
rate  of  still-births  during  the  year.  The  ratio  of  still-births 
to  living  births  is  much  greater  for  illegitimate  than  for  legiti- 
mate children,  especially  among  mothers  less  than  twenty 
years  of  age.  There  are  marked  differences  in  the  still-birth 
rates  in  different  countries. 

At  Johnstown,  Pa.,  4.5  per  cent  of  all  births  were  still- 
births, and  8.7  per  cent  of  all  mothers  reporting  had  suffered 
miscarriages. 

The  percentages  of  still-births  arranged  according  to  the 
age  of  the  mothers  gave  the  very  high  percentage  of  11.1 
per  cent  for  mothers  under  20  years  of  age,  4  per  cent  for  age 
group  20-24,  5.1  for  25-29  years,  4.4  for  30-39  years,  and  3.3 
for  ages  over  40.  The  percentage  for  native  mothers  was 
5.2  per  cent,  for  foreign  mothers,  3.8  per  cent. 

Infant  mortality  and  the  specific  death-rate  for  infants.  — 
There  are  two  reasons  why  the  specific  death-rate  for  age 
group  0-1  year  is  not  used  more.  The  first  is  the  difficulty 
of  finding  the  actual  number  of  infants  alive  at  the  middle  of 
any  calendar  year.  Of  course,  a  census  might  be  taken  on 
July  1,  but  even  that  figure  would  not  be  very  satisfactory 
for  births  are  not  uniformly  distributed  through  the  year 
and  the  ages  of  infants  are  often  given  incorrectly.  It  is 
possible  to  compute  the  number  alive  July  1  from  the 
monthly  records  of  births  and  deaths,  but  rarely,  if  ever,  in 
this  country  are  the  data  for  doing  this  published.  The 
reports  of  vital  statistics  of  Hamburg  contain  each  year  a 
table  like  that  shown  in  Table  97  from  which  this  computa- 
tion can  be  made. 

Starting  in  1911  we  see  that  in  January  1853  children  were 
born,  of  which  260  died  the  same  year;  5,  however,  died  in 
January,  1912,  before  reaching  their  first  birthday.  Of  the 
children  born  in  February,  1911,  8  died  in  January,  1912, 
and  3  in  February,  1912.  By  keeping  up  this  tabulation  we 


342 


STUDIES  OF  DEATHS  BY  AGE  PERIODS 


TABLE  97 

BIRTHS  AND  DEATHS  OF  CHILDREN  UNDER  ONE  YEAR 
Hamburg,  1911  and  1912 


Year 
and 
mo. 

Births. 

Died 
in 
1911. 

Died  in  1912  before  reaching  age  of 
one  year. 

Total 

Died 
in 
first 
year. 

Reached 
the  first 
year  alive. 

Ut 

I1" 

Jar 
191 

J. 

F. 

M. 

A. 

M. 

J. 

J. 

A. 

S. 

O. 

N. 

D. 

No. 

% 

(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

(7) 

(«. 

(9) 

(10) 

Hi) 

(12) 

13 

14) 

(15) 

d«) 

(17) 

(18; 

(    ) 

(2( 

1911. 
Jan. 
Feb. 
Mar. 
April 
May 
June 
July 
Aug. 
Sept 
Oct. 
Nov. 
Dec. 

.  1,853 
1,700 
1,752 
1,713 
1,777 
1,670 
,791 
,760 
,670 
,668 
,603 
,705 

260 
254 
253 
250 
251 
242 
255 
188 
124 
131 
90 
58 

5 

8 
4 
6 
11 
11 
14 
15 
IS 
19 
27 
53 

2 

5 
11, 
16 
25> 
31 
45 
62, 
70 
73 
99 
133 
179 

265 
265 
269 
275 
282 
287 
317 
258 
197 
230 
223 
237 

1,588 
1,435 
1,483 
1,438 
1,495 
1,383 
1,474 
1,502 
1,473 
1,438 
1,380 
1,468 

85.70 
84.41 
84.65 
83.95 
84.13 
82.81 
82.30 
85.34 
88.20 
86.21 
86.09 
86.10 

84.97 

1,5 
1,5 
1.& 
1,5 
1,5 
1,5 
1,6 
1,6 
1,6 
1,6 
1,5 
1,7 

3 
6 
\ 

3 
8 
8 
10 
11 
18 
27 
27 

6 
12 
10 
11 
<J 
12 
8 
17 

s 

25 

3 
43 
7 
10 
6 
8 
li 
16 
14 

8 
4 
9 

11 
14 

8 

10 

0 

13 
8 
6 
5 

15 
7 

4 

6 
2 

S 
it 
13 

4 
4 

8 

9 

i) 

0 
3 

10 

3 
0 

Sum 

20,662 

2356 

11)1 

12,5 

118 

74 

67 

54 

42 

32 

18 

17 

9 

9 
6 
15 
0 
13 
7 
16 
20 
25 
38 
69 

2 

3 
3 
6 
8 
8 
12 
11 
21 
22 
33 
35 
70 

749 

3105 

17,557 

1912. 
Jan. 
Feb. 
Mar. 
April 
May 
June 
July 
Aug. 
Sept. 
Oct. 
Nov. 
Dec. 

1,829 
1,722 
1,810 
1,721 
1,723 
1,777 
1,833 
1,817 
1,748 
1,781 
1,688 
1,799 

78 

45 

56 

30 
44 
63 

19 
20 
29 
57 

17 
12 
21 

37 
76 

13 
15 

20 
17 
26 
60 

12 

15 
15 
20 
20 

41 

68 

9 
15 
19 
19 
28 
26 
43 
70 

8 
9 
7 
6 
12 
21 
21 
25 
67 

4 
4 

6 
7 
12 
19 
19 
30 
27 
71 

247 
199 
201 
177 
195 
186 
178 
166 
141 
142 
104 
70 

Sum 

21,248 

78 

101 

137 

125 

163 

151 

191 

229 

176 

199 

224 

232 

2006 

19,2 

Died  in  year  1912.  . 

269 

22f> 

255 

199 

230 

205 

233 

261 

194 

216 

233 

234 

2755 

FIRST-YEAR  DEATH-RATE  343 

obtain  all  the  deaths  in  1912  of  babies  born  in  1911.  In  the 
same  way  we  obtain  the  deaths  in  1912  of  infants  born  in 
1912.  These  added  to  the -preceding  give  us  all  the  infant 
deaths  for  1912,  namely,  2755.  The  number  of  children 
living  Jan.  1,  1913,  was  21,248  -  2006,  or  19,242.  By 
starting  with  July  1,  1910,  we  could  obtain  the  number  of 
children  living  July  1,  1912.  It  requires  monthly  records 
extending  over  two  years  to  get  this  result,  and  even  after 
we  get  it  it  may  not  be  exact  as  there  may  have  been  errors 
in  the  records. 

The  infant  mortality  is  much  simpler  to  compute,  but  it  is 
not  without  its  errors.  Birth  reporting  is  notoriously  bad, 
and  there  is  often  doubt  as  to  the  stated  age  of  the  dying 
child.  Children  within  a  few  months  of  their  first  birthday 
are  sometimes  said  to  be  a  year  old. 

In  the  long  run,  the  average  specific  death-rates  for  age 
group  0-1  agree  fairly  well  with  the  infant  mortalities,  but 
in  any  particular  place  and  year  they  may  vary  from  each 
other  as  much  as  twenty-five  or  fifty  per  cent.  The  infant 
mortality  should  be  stated  in  whole  numbers  as  the  accuracy 
of  the  data  does  not  warrant  the  use  of  decimals. 

The  deaths  of  infants  in  one  year  will  include  some  who 
were  born  in  the  preceding  year.  In  our  infant  mortality 
ratios,  therefore,  we  are  not  dealing  wholly  with  the  same 
infants  in  the  denominator  and  numerator.  Fluctuations 
in  the  birth-rate  in  successive  years  may  influence  this 
ratio. 

First-year  death-rate.  —  In  the  case  of  Hamburg  we  see 
from  the  table  that  in  the  year  1912  there  were  21,248  births 
and  2755  infant  deaths.  From  these  figures  we. may  compute 
the  infant  mortality  ratio  in  the  usual  way  and  obtain  130 
per  1000.  Yet  if  we  consider  the  20,662  births  in  the  twelve 
months  of  1911  and  follow  them  through  their  first  year,  we 
find  that  3105  died,  that  is  the  ratio  was  150  per  1000.  In 


344 


STUDIES  OF   DEATHS  BY  AGE  PERIODS 


other  words,  850  per  1000,  or  85  per  cent  reached,  their  first 
year  of  life. 

In  the  printed  table  we  find  in  the  last  column  for  1911 
figures  which  show  these  percentages  by  months.  It  is 
interesting  to  notice  how  this  percentage  of  born  children 
who  reach  their  first  year  varies  with  the  season.  According 
to  the  1911  figures  for  Hamburg,  September  is  the  most 
favorable  month  for  a  birth  because  88.2  per  cent  of  the 
children  born  that  month  reached  the  age  of  one  year;  118 
per  thousand  died!  July  is  the  most  unfavorable  month  as 
only  82.3  per  cent  reached  the  first  year;  177  per  thousand 
died. 

Very  few  American  cities  keep  their  records  in  such  shape 
that  facts  like  these  can  be  easily  secured.  In  Hamburg  they 
publish  both  the  infant  mortality  rates  and  the  percentage 
of  infants  who  die  in  their  first  year  of  life.  They  also  pub- 
lish the  proportionate  infant  mortality,  that  is,  the  per  cents 
which  the  infant  deaths  are  of  the  total  deaths.  It  is  in- 
teresting to  compare  these  figures. 

TABLE  98 
INFANT  DEATHS,  HAMBURG 


Year. 

Proportionate 
mortality. 

Infant  mortality  (per 
1000  births.) 

Number  of  infants  per 
1000  who  died  in  their 
first  year. 

(1) 

(2) 

(3) 

(4) 

1908 

26.2 

156  . 

184 

1909 

23.7 

142 

159 

1910 

24.4 

149 

160 

1911 

23.4 

158 

159 

1912 

20.8 

130 

141 

This  method  of  studying  infant  mortality  by  determining 
the  percentage  of  first-year  deaths  was  used  in  the  Johns- 
town, Pa.,  investigation  in  1914.  It  was  here  referred  to  as 


REDUCTION  IN  INFANT  MORTALITY  345 

the  "absolute  infant  mortality,"  the  conventional  method 
of  comparing  births  and  infant  deaths  for  a  calendar  year 
being  regarded,  as  indeed  it  is,  as  an  approximate  method, 
chosen  for  convenience  only.  In  Johnstown  the  results  were 
obtained  by  an  intensive  study  of  individual  infants.  Con- 
trary to  the  results  in  Hamburg  the  "percentage  of  first-year 
deaths"  was  less  than  the  "infant  mortality,"  the  figures 
being  13.4  per  cent  (134  per  1000)  and  165  respectively. 

Various  methods  of  stating  infant  mortality.  —  It  will  be 
seen  that  infant  mortality  may  be  expressed  in  various 
ways : 

1.  Rate  of  deaths  in  first  year — the  true,  or  "absolute," 

method. 

2.  Infant  mortality,  the  calendar  ratio  between  infant 

deaths  and  births  —  the  common  method. 

3.  Specific  death-rate  for  age-group  0-1  year  —  difficult 

to  compute,  but  useful  as  hereafter  shown. 

4.  Proportionate  mortality  —  the  ratio   between  infant 

deaths  and  total  deaths. 

5.  Infant  death-rate  per  1000  inhabitants  —  a  ratio  rarely 

used  and  of  little  value. 

It  should  be  noticed  that  all  of  these  ratios  except"  the  first 
are  calendar  ratios,  that  is,  they  are  based  on  one  year  or 
some  other  interval  of  time.  The  true  rate  of  infant  deaths 
considers  the  calendar  only  as  to  births,  the  period  covered 
by  the  deaths  being  one  year  from  the  date  of  each  birth. 
In  the  following  paragraphs  all  of  these  ratios  are  used  in 
order  that  the  student  may  learn  to  discriminate  between 
them. 

Chronological  reduction  in  infant  mortality.  —  The  infant 
mortality  rates  in  nearly  all  civilized  countries  are  falling. 
In  recent  years  the  fall  has  been  more  rapid  than  it  was  a 
generation  ago.  In  Sweden  we  have  a  very  long  record,  a 
part  of  which  is  given  in  Table  99.  Prior  to  1800  the  infant 


346 


STUDIES  OF  DEATHS  BY  AGE  PERIODS 


TABLE  99 

INFANT  AND  CHILD  MORTALITY  IN  SWEDEN 
1761  to  1900  by  6-Year  Periods 


Period. 

Total  death- 
rate  per  1000. 

Age-group  in  years. 

O-l.1 

1-3.2 

3-5.2 

0-5.2 

(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

1751-55 

26.52 

205.75 

52.17 

27.31 

86.07 

1756-60 

28.25 

203.41 

49.50 

26.26 

81.64 

1761-65 

29.08 

221.73 

53.94 

28.49 

90.46 

1766-70 

26.38 

210.41 

50.12 

27.06 

85.14 

1771-75 

33.07 

212.89 

66.55 

36.15 

92.88 

1776-80 

24.86 

192.02 

56.21 

29.13 

83.74 

1781-85 

27.80 

193.98 

62.64 

36.16 

86.44 

1786-90 

27.61 

205.70 

48.78 

23.04 

81.67 

1791-95 

25.21 

192.59 

44.63 

20.76 

77.09 

1796-00 

25.65 

199.53 

48.02 

23.47 

79.55 

1801-05 

24.35 

186.08 

41.48 

18.70 

70.65 

1806-10 

31.45 

211.46 

59.09 

29.09 

87.42 

1811-15 

27.11 

191.76 

56.46 

20.57 

81.54 

1816-20 

24.63 

175.51 

45.93 

17.96 

71.00 

1821-25 

22.07 

158.85 

36.24 

14.33 

61.63 

1826-30 

25.10 

175.76 

37.72 

17.07 

64.53 

1831-35 

23.05 

167.31 

33.44 

14.44 

60.32 

1836-40- 

22.53 

166.35 

35.47 

15.42 

60.31 

1841-45 

20.20 

153.77 

30.38 

14.39 

56.18 

1846^50 

20.95 

152.56 

33.39 

16.48 

57.34 

1851-55 

21.65 

148.89 

35.32 

18.79 

58.83 

1856-60 

21.73 

143.47 

39.12 

23.87 

61.96 

1861-65 

19.76 

136.17 

40.95 

21.78 

58.48 

1866-70 

20.54 

141.93 

38.78 

19.59 

56.14 

1871-75 

18.28 

133.57 

29.78 

14.64 

51.47 

1876-80 

18.26 

126.28 

36.26 

19.80 

53  01 

1881-85 

17.53 

116.08 

31.82 

17.09 

47.18 

1886-90 

16.37 

105.00 

25.88 

13.41 

40.06 

1891-95 

16.61 

102.76 

23.97 

12.65 

38.21 

1896-00 

16.12 

100.50 

21.78 

9.72 

35.65 

1  Per  1000  births  during  the  given  period,  i.e.,  "  infant  mortality." 

2  Per  1000  of  population  at  middle  of  period,  i.e.,  specific  death-rates. 


REDUCTION  IN  INFANT  MORTALITY 


347 


mortality  was  upwards  of  200,  but  by  1900  it  was  only  about 
half  as  much.     In  Stockholm  in  1912  it  was  only  82. 

In  Massachusetts  l  the  rate  of  infant  mortality  has  varied 
as  follows: 

TABLE  100 
RATE   OF  DEATHS  DURING  FIRST  YEAR 

Massachusetts 


Year. 

Per 

1000. 

Year. 

Per 

1000. 

Year. 

Per 

1000. 

Year. 

Per 

1000. 

Year. 

Per 

1000. 

(1) 

(2) 

(1) 

(2) 

(1) 

(2) 

(1) 

(2) 

(1) 

(2) 

1851 

133 

1864 

154 

1877 

152 

1890 

•167 

1903 

138 

1852 

126 

1865 

147 

1878 

150 

1891 

162 

1904 

133 

1853 

135 

1866 

138 

1879 

145 

1892 

162 

1905 

140 

1854 

131 

1867 

136 

1880 

163 

1893 

164 

1906 

138 

1855 

135 

1868 

140 

1881 

163 

1894 

163 

1907 

133 

1856 

123 

1869 

149 

1882 

163 

1895 

156 

1908 

134 

1857 

118 

1870 

162 

1883 

159 

1896 

158 

1909 

127 

1858 

122 

1871 

151 

1884 

159 

1897 

147 

1910 

133 

1859 

130 

1872 

194 

1885 

157 

1898 

151 

1911 

119 

1860 

134 

1873 

178 

1886 

155 

1899 

150 

1912 

117 

1861 

146 

1874 

164 

1887 

160 

1900 

157 

1913 

110 

1862 

131 

1875 

175 

1888 

162 

1901 

138 

1914 

106 

1863 

150 

1876 

158 

1889 

160 

1902 

140 

1915 

102 

The  report  speaks  of  these  as  "first-year  deaths"  but 
does  not  state  how  they  were  computed.  Apparently  the 
figures  refer  to  infant  mortality  computed  in  the  conventional 
way.  The  figures  show  a  substantial  decrease  only  during 
the  last  ten  years. 

The  following  figures  show  the  decrease  in  infant  mortality 
computed  in  the  conventional  way  between  1908  and  1915 
for  Massachusetts,  Boston  and  the  remainder  of  the  state 
outside  of  Boston. 


Mass.  Registration  Report,  1915,  p.  153. 


348 


STUDIES  OF  DEATHS  BY  AGE  PERIODS 


TABLE  101 
INFANT  MORTALITY:    MASSACHUSETTS 


Year. 

Massachusetts. 

Boston. 

Remainder  of  state. 

(1) 

(2) 

(3) 

(4) 

1908 

134 

149 

129 

1909 

127 

121 

129 

1910 

133 

127 

134 

1911 

119 

126 

118 

1912 

117 

117 

116 

1913 

110 

110 

110 

1914 

106 

105 

107 

1915 

102 

104 

101 

It  would  be  possible  to  print  page  after  page  of  such  figures 
as  these  taken  from  the  records  of  our  American  cities. 

In  Boston  the  rate  of  infant  deaths  per  1000  of  total 
population  has  decreased  as  follows: 

TABLE  102 
INFANT  MORTALITY:   BOSTON 


Year. 

Rate  per  1000  of 
population. 

Year. 

Rate  per  1000  of 
population. 

(1) 

(2) 

(1) 

(2) 

1875 

6.6 

1895 

5.1 

1880 

5.6 

1900 

4.3 

1885 

5.5 

1905 

3.7 

1890 

5.1 

1910 

3.3 

This  ratio  is  one  which  depends  upon  the  number  .of 
children  born  as  well  as  upon  their  rate  of  death,  and  involves 
the  varying  composition  of.  the  population  as  to  age,  mar- 
riage, nationality,  and  so  on. 

Reasons  for  the  decreasing  infant  mortality.  —  As  most 
of  the  current  discussions  of  infant  deaths  are  based  on  the 


INFANT  MORTALITY  IN   DIFFERENT  PLACES     349 

calendar  ratio  between  reported  deaths  of  infants  and  reported 
births,  it  is  well  to  remember  that  a  falling  ratio  may  result 
from  an  increase  in  the  denominator  as  well  as  from  a  decrease 
in  the  numerator  of  the  fraction.  We  have  already  learned 
that  the  birth  registration  is  increasing  in  accuracy,  that  a 
larger  percentage  of  births  are  reported  now  than  formerly. 
This  fact  alone  will  account  for  a  part  of  the  drop  in  infant 
mortality;  in  some  places  it  may  account  for  nearly  all  of  it. 
In  comparing  the  infant  mortality  rates  in  different  places 
this  difference  in  the  relative  accuracy  of  reports  of  births 
and  deaths  must  not  be  overlooked.  To  understand  just 
what  is  being  accomplished  by  present-day  activities  in 
infant  welfare  it  is  necessary  to  dig  deeper  into  the  subject 
and  to  analyze  the  statistics  of  infant  births  and  deaths. 

Infant  mortality  in  different  places.  —  If  we  examine  the 
statistics  for  different  countries  we  shall  discover  great 
differences  in  infant  mortality.  We  have  space  here  for  only 
a  few  figures. 


350 


STUDIES  OF  DEATHS  BY  AGE  PERIODS 


TABLE   103 
INFANT  MORTALITY  IN  A  FEW  FOREIGN  CITIES 


Cities. 

1881- 
1885. 

1886- 
1890. 

1891- 
1895. 

1896- 
1900. 

1901- 
1905. 

1906- 
1910. 

1911. 

1912. 

**                   (1) 

(2) 

(3) 

(4) 

(5) 

(6) 

(7) 

(8) 

(9) 

London 

150 

153 

156 

162 

139 

114 

129 

91 

Edinburgh 

127 

136 

140 

144 

131 

119 

118 

113 

Dublin     (registration 
area)  

176 

175 

169 

175 

158 

146 

156 

140 

Sydney  

173 

155 

138 

130 

107 

85 

71 

76 

Melbourne 

171 

173 

136 

129 

113 

94 

78 

90 

Montreal  

246 

237 

258 

271 

261 

242 

Toronto  

200 

231 

205 

166 

114 

Paris  

162 

15? 

135 

119 

110 

106 

118 

103 

Amsterdam 

203 

199 

168 

146 

122 

90 

91 

64 

Rotterdam  

209 

207 

191 

167 

144 

105 

103 

79 

Stockholm  

208 

18? 

170 

169 

136 

103 

77 

8? 

Christiania 

156 

168 

158 

152 

119 

96 

116 

107 

St.  Petersburg  .... 

301 

243 

242 

251 

246 

256 

231 

249 

Moscow  

340 

320 

316 

286 

262 

313 

321 

333 

Berlin 

279 

264 

242 

218 

202 

164 

173 

142 

Hamburg  

222 

260 

226 

182 

174 

150 

158 

130 

Vienna 

196 

196 

219 

195 

178 

172 

166 

149 

Prague 

218 

200 

194 

170 

163 

156 

186 

139 

Budapest  

244 

237 

199 

174 

149 

151 

161 

141 

Trieste 

212 

238 

233 

218 

201 

213 

215 

184 

Milan.  .  . 

156 

161 

158 

147 

146 

129 

? 

102 

Buenos  Aires  

185 

209 

151 

120 

93 

100 

105 

96 

INFANT  MORTALITY  IN  DIFFERENT  PLACES     351 

If  we  take  the  different  cities  of  the  United  States  we  shall 
find  ranges  of  infant  mortality  almost  as  great  as  in  the  cities 
of  different  countries.  In  1915  the  New  York  Milk  Com- 
mittee made  an  extensive  study  of  the  infant  mortality  rates 
of  144  United  States  cities.  The  minimum,  median  and 
maximum  rates  for  the  year  1915  were  as  follows: 


TABLE  104 
INFANT  MORTALITIES  IN  UNITED   STATES   CITIES 


Infant  mortality. 

Population  group. 

Number  of 
cities. 

Minimum. 

Median. 

Maximum. 

(1) 

(2) 

(3) 

«). 

(5) 

500,000- 

10 

82 

104 

120 

200,000-500,000 

20 

53 

84 

133 

100,000-200,000 

16 

47 

100 

182 

50,000-100,000 

31 

62 

98 

193 

30,000-  50,000 

31 

31 

86 

185 

20,000-  30,000 

21 

37 

98 

167 

These  figures  indicate  that  there  was  little  difference  in 
the  median  infant  mortality  between  the  large  and  the  small 
cities,  but  that  in  the  larger  cities  there  was  a  greater  uni- 
formity in  the  figures.  The  very  low  rates  as  well  as  the  very 
high  rates  were  found  in  relatively  small  cities.  The  in- 
accuracies of  the  birth  registration  may  account  for  many  of 
these  differences. 

We  may  go  even  further  and  take  the  different  wards  of  a 
single  city,  and  find  these  same  differences.  In  the  twenty- 
five  wards  of  Boston  in  1910  the  infant  mortalities  ranged 
from  75  to  210,  the  median  being  117  and  the  average  122. 
In  eleven  districts  of  Johnstown  in  1911  the  "absolute  infant 
mortality"  varied  from  50  to  271,  the  figure  for  the  entire 


352  STUDIES  OF  DEATHS  BY  AGE  PERIODS 

city  being  134.  And  in  the  same  way  we  could  find  differ- 
ences block  by  block.  In  any  intensive  study  it  is  of  funda- 
mental importance  to  find  out  the  geographical  location  of 
infant  deaths. 

Deaths  of  infants  at  different  ages.  —  A  year  is  a  long 
time  in  the  life  of  an  infant.  One  can  learn  no  more  from  a 
study  of  the  infant  mortality,  when  all  ages  up  to  one  year 
are  considered  together,  than  from  a  study  of  the  general 
death-rate  of  a  community  where  all  deaths  from  zero  to  a 
hundred  years  of  age  are  considered  together.  It  is  necessary 
to  study  the  infant  death-rate  by  months,  weeks  and  even 
days. 

The  need  of  such  study  is  obvious.  During  early  life 
many  of  the  deaths  are  from  troubles  incident  to  birth;  later 
the  question  of  feeding,  and  especially  of  the  effect  of  artificial 
food  becomes  important.  Some  of  the  welfare  activities  are 
directed  towards  one  end,  some  towards  another.  The 
establishment  of  milk  stations,  for  example,  might  affect  the 
death  of  weaned  babies,  but  have  little  influence  on  babies 
less  than  a  month  old.  There  are  many  things  which  will 
occur  to  the  reader  which  will  show  the  importance  of  this 
specific  information. 

Let  us  first  consider  some  of  these  subdivisions.  In  doing 
so,  we  may  use  several  of  the  methods  with  which  we  have 
already  become  familiar. 

In  Hamburg,  in  1912,  the  percentage  age  distribution  of 
infant  deaths  was  as  follows: 


DEATHS  OF  INFANTS  AT  DIFFERENT  AGES      353 


TABLE  105 
INFANT  DEATHS  AT  DIFFERENT  AGES:    HAMBURG 


Age-group, 
months. 

Per  cent  of  infant 
deaths  in  group. 

Age,  months. 

Per  cent  of  infants  who 
died  at  less  than 
'   stated  age. 

(1) 

(2) 

(3) 

(4) 

0+ 

38.5 

1 

38.5 

1+ 

12.3 

2 

50.8 

2+ 

9.8 

3 

60.6 

3+ 

8.4 

4 

69.0 

4+ 

6.1 

5 

75.1 

5+ 

.     4.7 

6 

79.8 

6+ 

4.3 

7 

84.1 

7+ 

4.4 

8 

88.5 

8+ 

3.0 

9 

91.5 

9+ 

2.9 

10 

94.4 

10+ 

2.6 

11 

97.0 

11+ 

3.0 

12 

100.0 

An  irregular  grouping  is  more  common,  because  of  the 
greater  importance  of  the  subdivisions  at  the  very  early  ages. 
Thus  for  Boston,  in  1912,  we  find  the  following  figures: 

TABLE  106 
AGE  DISTRIBUTION  OF  INFANT  DEATHS:    BOSTON,  1912 


Per  cent  of  infant 

Per  cent  of  infants 
who  died  at  less  than 

Age-group. 

Q6£ltJlS. 

Age. 

stated  age. 

Male. 

Female. 

Male. 

Female. 

Cl) 

(2) 

fi) 

(4) 

(5) 

(6) 

0-    days 

15.4 

11.2 

1  day 

15.4 

11.2 

1+  days 

4.0 

4.5 

2  days 

19.4 

15.7 

2+  days 

3.9 

2.4 

3  days 

23.3 

18.1 

3+  days 

6.8 

7.7 

1  week 

30.1 

25.8 

1+  weeks 

3.7 

4.9 

2  weeks 

33.8 

30.7 

2+  weeks 

5.4 

4.4 

3  weeks 

39.2 

35.1 

3+  weeks 

2.8 

2.5 

1  month 

42.0 

37.6 

1+  months 

10.9 

9.0 

2  months 

52.9 

46.6 

2+  months 

7.0 

9.5 

3  months 

59.9 

56.1 

3+  months 

18.1 

19.2 

6  months 

78.0 

75.3 

6+  months 

13.4 

13.6 

9  months 

91.4 

88.9 

9  to  1  year 

8.6 

11.1 

1  year 

100.0 

100.0 

0  to  1  year 

100.0 

100.0 

354 


STUDIES  OF  DEATHS  BY  AGE  PERIODS 


It  will  be  noticed  that  on  the  basis  of  the  summation 
results  of  the  last  column  the  figures  may  be  readily  compared 
with  those  for  Hamburg  where  the  figures  are  given  by 
regular  monthly  groups. 

The  important  fact  is  that  the  death-rate  of  infants  is 
much  higher  during  the  first  weeks  and  days  of  life  than  it  is 
after  the  first  six  months.  The  apparent  increase  from  the 
eleventh  to  the  twelfth  month,  often  found,  is  very  likely  due 
to  inaccuracies  in  stating  the  age  at  one  year  —  the  error  of 
round  numbers. 

Specific  death-rates  of  infants  at  different  ages.  —  A 
better  appreciation  of  the  early  infant  mortality  can  be 
obtained  by  studying  the  specific  death-rates  of  infants  at 
different  ages.  In  Glover's  United  States  Life  Tables  we 
find  the  following  figures  which  give  the  monthly  specific 
death-rates. 

TABLE  107 

SPECIFIC  DEATH-RATES   OF  INFANTS  BY  MONTHS,   1910 
Original  Registration  States  as  Constituted  in  1900 


Number  dying  in  age  interval  among  1000  alive  at  be- 
ginning of  age  interval. 

Age  interval,  months. 

Males. 

Females. 

(1) 

(2) 

(3) 

0-1 

48.94 

38.33 

1  + 

13.17 

10.44 

2  + 

10.91 

9.01 

3  + 

9.29 

7.82 

4  + 

8.21 

6.96 

5  + 

7.41 

6.36 

6+    ' 

6.76 

5.90 

7  + 

6.25 

5.47 

8  + 

5.81 

5.09 

9  + 

5.40 

4.74 

10  + 

5.03 

4.39 

11  + 

4.70 

4.04 

0  -  1  yr. 

124.95 

103.77 

INFANT  MORTALITY  BY  AGE  PERIODS 


355 


Expectation  of  life  at  different  ages.  —  The  expectation 
of  life  is  given  for  infants  as  follows: 


TABLE  108 

EXPECTATION   OF  LIFE1 
Original  Registration  States  as  Constituted  in  1900 


Average  length  of  life  remaining  to  each  one  alive  at  be- 
ginning of  age  interval.    Years. 

Age  interval,  months. 

Males. 

Females. 

(1) 

(2) 

(3) 

0-1 

49.86 

53.24 

1  + 

52.35 

55.28 

2  + 

52.96 

55.78 

3  + 

53.46 

56.20 

4  + 

53.88 

56.56 

5  + 

54.24 

56.87 

6  + 

54.56 

57.15 

7  + 

54.85 

57.41 

8  + 

55.11 

57.64 

9  + 

55.35 

57.85 

10  + 

55.57 

58.05 

11  + 

55.76 

58.22 

1  Based  upon  deaths  in  1909,  1910  and  1911. 

The  expectation  of  life  of  a  male  child  at  birth  is  about 
the  same  as  that  of  a  11-year  old  boy.  The  expectation  of 
life  increases  from  birth  to  about  the  third  year  when  it 
reaches  its  maximum. 

Infant  mortality  by  age  periods.  —  Another  way  of 
showing  the  infant  mortality  by  age  periods  is  to  find  the 
ratios  between  the  numbers  of  deaths  in  each  period  and  the 
total  number  of  births.  These  results  may  also  be  expressed 
cumulatively.  Thus  for  Boston,  in  1910,  we  have: 


356 


STUDIES  OF  DEATHS  BY  AGE  PERIODS 


TABLE   109 
INFANT  MORTALITY,   BOSTON,   1910 


Age  period. 

Deaths  per  1000 
births. 

Age  period. 

Deaths  per  1000 
births. 

(1) 

(2) 

(1) 

(2) 

0-2  days 

20 

0-2  days 

20 

2  days—  1  week   .  .  . 

12 

0-1  week 

32 

1  week—  1  month.   . 

16 

0-1  month.  . 

48 

1-3  months  
3-6  months  

21 
21 

0-3  months  
0-6  months  

69 
90 

6—9  months 

17 

0—  9  months 

107 

9-12  nfonths  

15 

0-1  year  

122 

Causes    of    infant    deaths.  —  In    Boston,  in    1910,  the 
principal  causes  of  infant  deaths  were  as  follows: 

TABLE  110 


Male. 

Female. 

(1) 

(2) 

(3) 

I.   General  diseases,  total  
Measles  

113 

16 

100 
12 

Diptheria  and  croup  

18 

8 

Whooping  cough 

8 

16 

Erysipelas 

10 

8 

Tubercular  meningitis  

15 

14 

Syphilis    

11 

12 

II.   Diseases  of  the  nervous  system,  total  .  .  . 
Meningitis  

47 
21 

47 
20 

Convulsions 

18 

16 

III.   Diseases  of  the  circulatory  system,  total. 
IV.   Diseases  of  the  respiratory  system  
Acute  bronchitis  .    

4 
209 
37 

4 
161 

30 

Broncho-pneumonia  
Pneumonia  
V.   Diseases  of  the  digestive  "system,  totals. 
Diseases  of  stomach,  except  cancer  
Diarrhea  and  enteritis  

88 
79 
355 
25 
320 

71 
56 
270 
12 
245 

VI.   Diseases  of  genito-urinary  system  
VIII.   Diseases  of  skin  and  cellular  tissue  
IX.   Diseases  of  bones,  etc  
X.   Malformations  . 

2 
8 
2 
69 

6 
2 
5 
61 

XI.   Early  infancy.  ... 

392 

319 

Congenital  debility  
XIII.   External  causes  

302 
9 

238 
7 

XIV.    Ill-defined  diseases  

m     j_     i    r                    11 

35 

32 

Number  of  deaths. 


INFANT   MORTALITY   BY   CAUSES 


357 


50 
0 

150 

100 


r 
3° 


50 


50 


Digestive  Diseases  Nos.  99-118 


Respirato 


Geuera 


Nervous 


y  Diseases 


Diseases  Nos.  1-59 


Diseases 


Ill-define  i  Diseases 


Nos.  86-96 


os,  60-76 


Nos.  187-9 


All  other  Diseases 
1908          1909          1910  1911          1912 

FIG.  54.  —  Infant  Mortality  by  Months,   Classified  According 
to  Cause:  Boston,  Mass. 


358  STUDIES  OF  DEATHS  BY  AGE  PERIODS 

Among  both  male  and  female  infants  37  per  cent  of  the 
deaths  were  from  malformations  and  diseases  of  early 
infancy;  about  27  per  cent  were  from  digestive  diseases; 
about  17  per  cent  were  from  respiratory  diseases.  Together 
the  deaths  from  these  causes  amounted  to  four-fifths  of  all 
the  infant  deaths.  These  percentages  are  not  constant. 
There  is  an  important  seasonal  variation;  there  are  also 
differences  according  to  age  and  nationality. 

In  1912,  Dr.  Wm.  H.  Davis  made  an  excellent  analysis  of 
the  infant  deaths  in  Boston  for  a  five-year  period.  Fig. 
54,  drawn  from  figures  in  his  report,  shows  how  the 
deaths  from  digestive  diseases  have  fallen  during  the  sum- 
mer season,  but  remained  almost  unchanged  during  the 
winter;  how  the  deaths  from  respiratory  diseases  are 
higher  in  the  winter  than  in  the  summer;  and  how  the 
deaths  from  diseases  of  early  infancy,  the  general  diseases 
and  nervous  diseases  do  not  have  a  marked  seasonal  dis- 
tribution. The  diagram  also  shows  how  the  diseases  from 
ill-defined  causes  have  decreased,  due,  it  is  said,  to  better 
diagnosis. 

In  Boston  the  diseases  were  classified  by  cause  and  age 
as  follows: 


INFANT  MORTALITY  BY  CAUSES 


359 


TABLE   111 
CAUSES  OF  INFANT  DEATHS:    BOSTON,   1910 


Cause 

iNumoer  ot  aeatns. 

| 

*i 

si 

Nj 

~§ 

4 

00  I 

*l 

OB 

T  "o 

*& 

|1 

ss 

(1) 

(2) 

(3) 

(4 

(5) 

(6) 

(7) 

(8) 

(9) 

I.   General  disease 

0 

1 

0 

1 

0 
0 
'   0 
0 
41 
305 
5 
0 
353 

2 

8 
1 
9 
10 
0 
0 
0 
32 
147 
0 
4 

21 
6 
2 
54 
41 
0 
3 
0 
24 
135 
2 
3 

37 
17 

4 
68 
153 
1 
0 
0 
11 
99 
3 
7 

43 
17 
1 
80 
201 
2 
3 
2 
7 
12 
4 
33 

58 
24 
0 
89 
112 
2 
2 
3 
3 
8 
1 
15 

52 
21 
0 
69 
108 
3 
2 
2 
2 
5 
1 
5 
270 

213 
94 
8 
370 
625 
8 
10 
7 
120 
711 
16 
67 
2249 

II.   Nervous  system 

III.   Circulatory  system.  .  .  . 
IV.   Respiratory  system  .  .  . 
V.   Digestive  system  
VI.   Genito-urinary  system 
VIII.   Skin  and  tissue 

IX.   Bones 

X.   Malformations  
XI.   Early  infancy 

XIII.   External  causes  .... 

XIV.   Ill-defined  causes  

All  causes  ...    . 

213 

292 

400 

405 

317 

As  would  be  expected  from  the  definition  the  largest  num- 
bers of  deaths  from  causes  incident  to  early  infancy  occur 
among  early  infants.  This  is  true  also  of  malformations. 
The  intestinal  diseases  reach  their  maximum  effect  between 
the  third  and  fifth  month,  the  respiratory  diseases  and  the 
general  diseases,  which  are  chiefly  communicable,  a  little 
later  —  say  between  the  sixth  and  eighth  months. 

In  Johnstown  important  differences  were  noted  between 
the  causes  of  death  among  infants  of  native  and  foreign 
mothers.  Thus,  during  the  first  year  of  life  the  following 
absolute  infant  mortalities,  with  subdivisions  by  cause  were 
found. 


360 


STUDIES  OF   DEATHS  BY  AGE  PERIODS 


TABLE   112 
CAUSES  OF  INFANT  DEATHS:    JOHNSTOWN 


Native 
mothers. 

Foreign 
mothers. 

(1) 

(2) 

(3) 

All  causes 

104 

171 

Diarrhoea  and  enteritis 

21 

54 

Respiratory  diseases  .  .                         

23 

48 

Premature  births  
Congenital  debility  or  malformations.  .  .  . 
Injuries  at  birth  

14 
6 

7 

20 
21 

2 

Other  cause,  or  not  reported  

33 

26 

In  Boston  the  following  figures  were  given  for  1910  for 
deaths  of  infants  born  to  native  and  foreign  mothers: 


TABLE  113 
CAUSES  OF  INFANT  DEATHS:    BOSTON 


JJ 
l| 

Canadian 
mothers. 

Irish 
mothers. 

Italian 
mothers. 

Russian 
mothers. 

(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

Congenital  debility  and  malfor- 
mations . 

50 

31 

49 

24 

20 

Diarrhoea  and  enteritis  

34 

37 

43 

22 

19 

Pneumonia   and   broncho-pneu- 
monia 

15 

18 

12 

29 

16 

Diseases  of  early  infancy  
Tuberculosis 

10 
2 

13 

4 

16 

1 

4 
2 

7 
2 

Measles,  scarlet  fever,  whooping 
cough  and  diphtheria.  .  .  . 

3 

3 

3 

8 

4 

Rates  per  1000  births 


THE  JOHNSTOWN  STUDIES 


361 


The  Johnstown  studies.  —  In  1915  the  Children's  Bureau 
of  the  U.  S.  Department  of  Labor,1  published  an  important 
intensive  study  of  the  Infant  Mortality  of  Johnstown,  an 
industrial  city  of  Pennsylvania.  Miss  Julia  C.  Lathrop  is 
the  Chief  of  this  bureau.  The  field  work  was  in  charge  of 
Miss  Emma  Duke.  This  was  essentially  a  sociological 
study.  Only  a  few  of  the  simple  correlations  can  here  be 
presented.  The  report  is  one  which  the  student  may  profit- 
ably read  in  full. 

TABLE  114 
INFANT  MORTALITY  AND   TYPE   OF  HOME 


Housing  condition. 

Infant 
mortality. 

(1) 

(2) 

Clean,  dry  

105 

"        damp.  . 

127 

Moderately  clean,  dry  

171 

"      damp  
Dirtv.  dry 

158 
162 

damp 

204 

Water  supply  in  house  

118 

Water  supply  outside  

198 

Water  closet 

108 

Yard  privy. 

159 

1  Infant  Mortality  Series  No.  3. 


362 


STUDIES  OF  DEATHS  BY   AGE  PERIODS 


TABLE   115 
INFANT  MORTALITY  AND   SLEEPING  ROOMS 


Infant     • 

mortality. 

(1) 

(2) 

Number  of  others  sleeping  in 
same  room  with  baby: 
2  or  less  

67 

3  to  5  

98 

Over  5  

123 

Baby  sleeping  in  separate  bed: 
Yes  

56 

No  

109 

TABLE   116 
INFANT  MORTALITY  AND  VENTILATION 


Ventilation  of  baby's  room. 

Infant 
mortality. 

(1) 

(2)  .. 

Good 

28 

Fair.    ... 

92 

Poor  

169 

TABLE   117 
INFANT  MORTALITY  AND  ATTENDANT  AT  BIRTH 


Infant 
mortality. 

(1) 

(2) 

Physician 

100 

Midwife  .  . 

180 

THE  JOHNSTOWN  STUDIES 


363 


TABLE  118 

INFANT  MORTALITY  AND  EDUCATION  OF 
FOREIGN  MOTHERS 


Infant 
mortality. 

(1) 

(2) 

Literate  

148 

Illiterate  .  .  .  ^  

214 

Speak  English 

146 

Do  not  speak  English 

187 

TABLE  119 
INFANT  MORTALITY  AND  AGE   OF.  MOTHER 


Age  of  mothers. 

Infant 
mortality. 

(1) 

(2) 

Under  20.  . 

137 

20-24  

121 

25-29  

143 

30-39  

136 

40  and  over 

149 

The  study  of  feeding  was  made  by  months.  The  following 
figures  show  the  rate  of  mortality  per  1000  babies  alive  at 
the  specified  time. 


364 


STUDIES  OF  DEATHS  BY  AGE  PERIODS 


TABLE   120 
INFANT  MORTALITY  AND  FEEDING 


Age. 

Specific  infant  mortality  (absolute) 

Breast  feeding 
only. 

Mixed  feeding. 

Artificial  feed- 
ing only. 

(1) 

(2) 

(3) 

(4) 

Second  month  

72 
54 
47 
38     • 
26 
29 
26 
18 
14 

78 
92 
57 
40 
32 
22 
20 
16 
11 

237 
217 
166 
127 
92 
72 
53 
25 
11 

Third                

Fourth 

Fifth 

Sixth                 

Seventh            

Eighth        '     

Ninth 

Tenth 

In  the  early  ages  the  difference  between  deaths  of  breast- 
fed infants  and  those  artificially  fed  is  very  great,  but  the 
difference  becomes  less  as  the  baby  grows  older. 


TABLE  121 
INFANT  MORTALITY  AND   HOUSEHOLD   DUTIES 


Household  duty. 


Infant  mortality. 


(1) 

(2) 

Cessation  of  duties  before  confinement: 
None  or  less  than  one  month                

137 

One  or  more  months  

113 

Time  of  resuming  all  household  duties  after  con- 
finement: 
8  days  or  less  

169 

9  to  13  days  :  

165 

14  days  or  more 

117 

OTHER  STUDIES  OF  THE  CHILDREN'S  BUREAU     365 

TABLE   122 
INFANT  MORTALITY  AND  EARNINGS   OF  FATHER 


Annual  earnings  of  husband. 

Infant  mortality. 

Native  wives. 

Foreign  wives. 

(1) 

(2) 

(3) 

Under  $521 

251 
162 
130 
167 
152 

$521  to  $624 

146 
70 
131 
76 

$625  to  $779        

$780  to  $899  

$900  to  $1199  

$1200  or  more 

Ample  

78 

108 

The  report  also  contains  statistics  relating  to  reproductive 
histories  of  the  mothers  studied  during  the  investigation. 

Other  studies  of  the  Children's  Bureau.  —  Besides  the 
Johnstown  studies,  here  emphasized  because  they  were  first 
made,  the  Children's  Bureau  has  made  at  this  writing  (1918), 
intensive  studies  in  Manchester,  N.  H.,  Saginaw,  Mich., 
Waterbury,  Conn.,  Brockton  and  New  Bedford,  Mass.,  Ak- 
ron, Ohio,  and  Baltimore.  A  brief  account  of  these  most 
important  intensive  investigations,  based  on  a  first-hand 
collectio.n  of  the  facts  may  be  found  in  the  Quarterly  Publica- 
tion of  the  American  Statistical  Association.1 

Two  tables  from  this  report  are  of  interest : 


1  Robert  M.  Woodbury,  Infant  Mortality  Studies  of  the  Children's 
Bureau,  June  1918,  pp.  30-53. 


366 


STUDIES  OF  DEATHS  BY  AGE  PERIODS 


TABLE   123 

INFANT  MORTALITY  AND  FATHER'S  EARNINGS, 
BALTIMORE 


Earnings  of  father  per 
year. 

True  infant 
mortality  rate. 

Earnings  of  father  per 
year. 

True  infant 
mortality  rate. 

(1) 

(2) 

(1) 

(2) 

No  earnings 

207.7 

$1050-1249 

66.6 

Under  $450 

156.7 

1250-1449 

.    74.0 

$450-1549 

118.0 

1450-1849 

86.3 

550-  649 

108.8 

1850  and  more 

37.2 

650-  849 

96.06 

Not  reported 

140.2 

850-1049 

71.5 

All  classes 

103.5 

TABLE   124 

INFANT  MORTALITY  AND   ORDER  OF  BIRTH  —  MOTHERS 
OF  ALL  AGES 


Number  of  birth 
in  order. 

True  infant  mortality. 

Number  of  birth 
in  order. 

True  infant  mortality. 

(1) 

(2) 

(1) 

(2) 

1 

115.8 

7 

128.2 

2 

102.7 

8 

162.6 

3 

111.5 

9 

142.1 

4 

127.0 

10 

181.1 

5 

129.3 

11 

146.8 

6 

132.2 

Although  in  general  the  average  infant  mortality  is  less  for 
the  second  child  than  for  the  first  or  subsequent  children, 
this  is  a  matter  which  varies  somewhat  with  the  age  of  the 
mother.  For  mothers  under  twenty  the  mortality  is  lowest 
for  first  children;  for  mothers  aged  30-34  years  it  is  lowest 
for  the  third  children;  and  for  mothers  aged  35-39  it  is 
lowest  for  fourth  children.  Perhaps,  if  nationality  were 
considered,  other  differences  would  be  noticed. 


MATERNAL  MORTALITY  367 

Infant  mortality  problems.  —  There  are  many  practical 
)roblems  relating  to  infant  mortality  which  must  be  studied 
vith  the  aid  of  statistics.  The  object  of  the  tables  here 
^ven  is  to  show  the  complexity  of  the  problem  and  the 
utility  of  depending  alone  upon  the  current  approximate 
nethod  of  stating  infant  mortality.  Extensive  compilations 
)f  data  for  various  places  and  for  different  years  make  easy 
•eading  and  give  one  a  superficial  knowledge  of  the  subject, 
)ut  they  do  not  help  us  very  much  in  solving  real  problems, 
it  is  the  intensive  studies  which  count.  What  kind  of  wel- 
are  work  deserves  the  largest  appropriations?  The  answer 
lepends  upon  where  the  babies  are  dying,  at  what  age  they 
ire  dying,  under  what  social  conditions,  under  what  remedi- 
ible  conditions,  and  so  on.  Are  the  milk  stations  of  our  large 
;ities  a  paying  life-saving  agency?  The  answer  cannot  be 
old  by  comparing  the  conventional  infant  mortality  rates; 
>erhaps  the  reduction  of  infant  mortality  may  be  among  the 
earliest  weeks  of  life,  an  age  at  which  artificial  feeding  is  less 
:ommon.  What  relation  is  there  between  density  of  popu- 
ation  and  infant  mortality?  The  answer  cannot  be  found 
vithout  splitting  up  the  infant  mortality  into  its  constituent 
>arts. 

The  lesson  is  one  which  the  author  wishes  to  teach  in  every 
ihapter  of  this  book,  namely,  that  the  vital  statistician  must 
,rain  himself  to  analyze  his  statistics;  to  be  specific;  to  think 
irst  what  kind  of  facts  he  needs  in  order  to  answer  a  specific 
question  and  then  go  after  them,  remembering  that  a  small 
lumber  of  well-directed  statistics  are  worth  more  than  vast 
lumbers  of  general  statistics,  piled  together  without  regard 
o  internal  differences  which  may  make  them  worthless. 

Maternal  mortality.  —  Closely  associated  with  infant 
nortality  we  have  the  problem  of  maternal  mortality. 
Since  the  long-a^o  studies  of  Dr.  Oliver  Wendell  Holmes, 
)ut  especially  since  the  rise  of  bacteriology,  there  has  been 


368 


STUDIES  OF   DEATHS  BY  AGE  PERIODS 


a  very  great  decrease  in  death-rates  from  child-bed  fever, 
but  even  within  very  recent  years  we  can  see  an  added 
improvement,  which  can  be  attributed  to  the  general  at- 
tention being  given  to  pre-natal  care,  to  laws  in  regard  to 
mid-wives  and  similar  causes.  The  following  condensed 
figures  for  New  York  city l  illustrate  this  decrease. 

TABLE  125 
MATERNAL  MORTALITY-RATE,   CITY  OF  NEW  YORK 


Quinquennial 
period. 

Rate  per  100,000  females  (age 
15-45). 

Puerperal 
sepsis. 

Other  deaths. 

(1) 

(2) 

(3) 

1898-1902 
1903-1907 
1908-1912 
1913-1917 

25.9 
26.1 
18.3 
15.3 

40.5 
.      41.3 
35.7 

29.8 

These  figures  might  more  properly  have  been  based  on 
married  women  within  the  given  ages,  or  upon  births  and 
still-births  taken  together  instead  of  on  all  females  of  child- 
bearing  age,  but  the  chronological  differences  are  so  great 
as  to  leave  no  room  for  doubt  as  to  the  main  facts. 

Childhood  mortality.  —  The  period  of  life  between  the 
ages  of  one  and  five  years  represents  a  peculiar  environment 
which  may  be  described  by  the  words  home  and  play.  In 
this  period  the  physiological  influence  of  the  mother  on  the 
child  becomes  less,  but  her  intelligence,  her  social  and 
economic  condition,  the  general  environment  of  the  house 
and  the  neighborhood  become  greater.  During  these  four 
years  the  specific  death-rate  of  children  decreases  greatly  and 
the  diseases  to  which  they  are  subject  change  in  character. 
1  Weekly  Bulletin,  Dept.  of  Health,  March,  1918. 


DISEASES  OF  EARLY  CHILDHOOD 


369 


TABLE  126 

SPECIFIC  DEATH-RATES  OF  CHILDREN1 
U.  S.  Registration  Area,  1910-1915 


Rate  per  1000 

Aee 

Male. 

Female. 

(1) 

(2) 

(3) 

0  —  1  year 

125.8 

101.1 

1  + 

27.3 

25.0 

2  + 

11.0 

10.1 

3  + 

6.9 

6.3 

4  + 

6.1 

4.7 

0-5  years 

36.0 

30.0 

5-9 

3.3 

3.0 

10-14 

2.3 

2.1 

1  From  Dr.  Dublin's  paper. 

The  diseases  which  occur  during  childhood  are  especially 
amenable  to  preventive  measures,  a  fact  which  makes  their 
study  one  of  especial  importance  from  the  standpoint  of  life 
saving. 

Diseases  of  early  childhood.  —  Dr.  Louis  I.  Dublin, 
Statistician  of  the  Metropolitan  Life  Insurance  Company 
has  discussed  these  diseases  in  an  article  on  the  Mortality  of 
Childhood,1  from  which  the  figures  for  proportionate  mortal- 
ity given  in  Table  127  are  taken. 

This  table  gives  only  those  diseases  for  which  the  propor- 
tionate mortality  was  more  than  3  per  cent  of  all  deaths. 
One  rather  unexpected  cause  of  death  looms  large  in  this 
table  —  namely,  burns.  In  the  second  year  of  life  the 
proportionate  mortality  was  1.7  per  cent,  the  next  year  4.3 
per  cent,  the  next  5.9  per  cent,  the  next  5.7  per  cent.  Dr. 

1  Quarterly  Publications,  Am.  Statistical  Assoc.,  March,  1918,  p.  921. 


370 


STUDIES  OF  DEATHS  BY  AGE  PERIODS 


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MORTALITIES  DURING  SCHOOL  AGE 


371 


Dublin  in  the  paper  referred  to  gives  the  specific  death-rates 
las  well  as  the  proportionate  mortalities.  The  figures  for 
burns  are  for  the  second  year  44.1  per  100,000,  for  the  third, 
44.8,  for  the  fourth,  39.4,  for  the  fifth,  28.1.  The  increasing 
importance  of  such  communicable  diseases  as  diphtheria, 
whooping  cough,  measles  and  the  like  during  this  period 
shows  the  increasing  influence  of  environment  and  associa- 
tion of  children  with  each  other. 

Proportionate  mortalities  during  school  age.  —  During 
the  ages  from  5  to  15  when  children  are  at  school  we  have 
what  is  perhaps  the  maximum  opportunity  for  contact 
infection.  During  these  ages,  therefore,  we  may  expect  to 
see  communicable  diseases  coming  to  the  front  in  our  pro- 
portionate mortalities.  But  we  also  find  weaknesses  in  the 
human  mechanism  making  themselves  felt.  Tuberculosis 
and  typhoid  fever  also  begin  to  loom  up  as  great  menaces. 


TABLE   128 

PROPORTIONATE   MORTALITY 
U.  S.  Registration  Area,  1910-15 


Ages  5-9. 


Per 
cent. 


Ages  10-14. 


Per 
cent. 


(I) 


(2) 


(3) 


(4) 


Diphtheria  and  croup.  .  .  . 

Scarlet  fever 

Pneumonia 

Organic  diseases  of  heart . 

Vehicular  accidents . . 

Typhoid  fever 

Broncho-pneumonia 

Tuberculosis  of  lungs 

Appendicitis 

Tuberculous  meningitis .  . 

Burns 

Drowning 

Measles .  . 


15.8 
7.1 
5.9 
4.4 
4.4 
3.7 
3.5 
3.5 
3.4 
3.4 
2.7 
2.6 
2.5 


Tuberculosis  of  lungs.  .  .  . 
Organic  diseases  of  neart. 

Typhoid  fever 

Appendicitis 

Diphtheria 

Pneumonia 

Drowning 

Vehicular  accidents 

Scarlet  fever 

Acute -articular  rheuma- 
tism . . 


10.2 
8.6 
6.4 
6.3 
5.6 
5.3 
4.4 
4.4 
3.0 

3.0 


372 


STUDIES  OF  DEATHS  BY  AGE  PERIODS 


Proportionate  mortalities  at  higher  ages.  —  The  following 
statistics  show  the  proportionate  mortalities  for  age-groups 
30-34,  50-54  and  70-74  years. 


TABLE   129 

PROPORTIONATE   MORTALITY 
U.  S.  Registration  Area,  1914,  Males 


Age  30-34  years. 

&i 

Age  50-54  years. 

u-*5 

®  c 

^OJ 

Age  70-74  years. 

£| 

(1) 

(2) 

32.0 
16.1 
6.9 
5.4 
5.2 
4.2 
4.1 
2.8 
2.8 
1.9 
1.6 

(3) 

(4) 

13.4 
11.7 
11.0 
8.1 
8.0 
7.7 
6.8 
3.2 
2.9 
.7 
.5 
.4 
.4 
.2 

(5) 

(6) 

Tuberculosis  
Accidents  

Tuberculosis  
Organic  diseases  of  heart 
Bright's  disease 

Organic     diseases     of 
heart  
Bright's  disease  
Apoplexy 

21.6 
13.4 
12.8 
8.4 
4.9 
4.5 
3.2 
2.8 
2.0 
1.9 
1.7 
1.6 
1.5 
1.5 
1.4 
0  9 

Pneumonia 

Organic  diseases  of  heart 
Angina  pectoris  
Suicide  
Bright's  disease 

Cancer  
Accidents 

Cancer 

Pneumonia  
Apoplexy  
Suicide 

Pneumonia  
Diseases  of  arteries  .  .  . 
Accidents  
Tubsrculosis 

Typhoid  fever 

Homicide  
Appendicitis  
Cancer  

Cirrhosis  of  liver  . 

Diabetes  
Paralysis  
Acute  endocarditis  
Pleurisy  

Old  age 

Broncho-pneumonia.  .  . 
Diseases  of  prostate.  .  .  . 
Paralysis  .*  
Cirrhosis  of  liver  
Diabetes 

Alcoholism 

Angina  pectoris  
Influenza 

Tuberculosis  stands  at  the  head  of  the  list  until  age  70. 
Organic  diseases  of  the  heart  increase  with  age.  Accidents 
diminish.  Bright's  disease  increases.  Suicide  decreases. 
Cancer  increases,  and  so  on. 

Of  course  in  a  complete  study  all  of  these  diseases  at 
different  ages  should  be  studied  by  the  use  of  specific  rates 
as  well  as  proportionate  mortality.  Studies  by  sex,  by 
season,  by  nationality,  and  so  on,  should  also  be  made. 

Average  age  of  persons  living.  —  The  average  age  of  a 
community  is,  of  course,  the  weighted  average  of  the  differ- 


MEDIAN  AGE  OF  PERSONS  LIVING  373 

ent  age-groups.  It  is  the  sum  of  the  ages  of  all  the  people 
divided  by  the  total  population. 

In  1880  the  average  age  of  the  aggregate  population  of 
the  U.  S.  registration  area  was  24.6  years,  in  1890  it  was 
25.6,  in  1900,  26.3  years.  There  has  apparently  been  an 
increase  although  the  figures  do  not  stand  for  exactly 
the  same  areas.  But  this  result  might  be  due  to  a  les- 
sening of  the  birth-rate,  to  an  increase  in  infant  mortal- 
ity, to  an  influx  of  ina  migrants  of  middle  age  or  to  a 
reduced  death-rate  among  the  aged.  That  the  native 
birth-rate  has  been  declining  is  true,  that  immigrants 
of  middle  age  have  been  entering  the  country  is  also 
true.  These  would  tend  to  increase  the  average  age.  But 
the  infant  mortality  has  been  decreasing,  not  increasing, 
and  the  mortality  in  the  higher  age-groups  has  rather  in- 
creased than  diminished.  These  factors  would  tend  to 
decrease  the  average  age.  Evidently  the  problem  is  so 
complicated  that  the  average  age  of  the  living  cannot  be 
fairly  taken  as  an  index  of  hygienic  conditions. 

Median  age  of  persons  living.  —  Instead  of  finding  the 
average  age  of  the  living  the  median  might  be  used,  but 
the  objections  to  the  average  age  of  the  living  would  apply 
also  to  the  median,  although  the  magnitude  of  their  in- 
fluence would  be  somewhat  different.  The  median  age  of 
the  population  of  the  United  States  has  greatly  increased 
during  the  last  century  as  the  following  figures  show: 


374 


STUDIES  OF  DEATHS  BY  AGE  PERIODS 


TABLE   130 
MEDIAN  AGE  OF  POPULATION:    UNITED  STATES 


Year. 

Median 
age. 

1800 

16.0 

1810 

16.0 

1820 

16.5 

1830  - 

17.2 

1840 

17.9 

1850 

19.1 

1860 

19.7 

1870 

20.4 

1880 

21.3 

1890 

21.9 

1900 

23.4 

1910 

24.4 

Average  age  at  death.  —  Nor  does .  the  average  age  at 
death  afford  a  fair  index  of  the  healthfulness  and  physical 
welfare  of  a  community.  The  reasons  are  similar  to  those 
just  mentioned.-  A  high  average  age  at  death  may  mean 
simply  that  the  birth-rate  is  low. 

There  has  been,  in  recent  years,  a  general  rise  in  the 
average  age  at  death.  In  Rhode  Island,  for  example,  the 
increase  has  been  as  follows: 

TABLE  131 
AVERAGE  AGE  AT  DEATH:    RHODE  ISLAND 


Period. 

Average  age  at 
death. 

Period. 

Average  age  at 
death. 

(1) 

(2) 

(3) 

'    (4) 

1861-65 
1866-70 
1871-75 
1876-80 

29.32 
32.42 
30.16 
31.21 

1881-85 
1886-90 
1891-95 
1896-00 

33.99 
33.42 
33.96 
34.53 

EXERCISES  AND  QUESTIONS  375 

In  1900  the  average  age  at  death  in  the  registration 
states  of  the  U.  S.  was  36.8  years.  For  the  cities  it  was 
32.4;  for  the  rural  districts  44.7  years.  In  Mass.,  in  1910, 
the  average  age  at  death  was  39.51.  In  1913  the  average 
age  at  death  for  the  U.  S.  Registration  Area  was  39.2  years 
for  males,  40.6  years  for  females,  and  39.8  years  for  the 
entire  population. 

In  a  general  way,  however,  the  prolongation  of  life  may  be 
regarded  as  an  index  of  human  progress,  as  Professor  W.  F. 
Willcox  has  pointed  out. 

EXERCISES  AND    QUESTIONS 

1.  Compare  the  infant  mortalities  for  certain  assigned  large  cities 
and  rural  districts. 

2.  Compare  the  infant  mortalities  for  California  cities  with  those  of 
eastern  cities. 

3.  Compute  the  seasonal  variations  of  infant  mortality  for  Cali- 
fornia cities. 

4.  What  is  the  average  infant  mortality  in  New  South  Wales?    Why 
is  it  so  low? 

6.  Do  the  statistics  of^  infant  mortality  justify  the  continuance  of 
the  milk  stations  in  New  York  City? 

6.  In  what  direction  will  efforts  to  reduce  infant  mortality  yield  the 
most  profitable  results? 

7.  Is  poverty,  ignorance,  race  or  climate  the  greatest  factor  in  causing 
high  infant  mortalities? 

8.  Make  a  statistical  study  of  some  cause  of  death,  to  be  assigned  by 
the  instructor,  according  to  age  periods. 


CHAPTER  XII 
PROBABILITY 

In  the  second  chapter  it  was  shown  that  the  average,  or 
mean,  of  a  number  of  figures  gave  a  very  inadequate  idea  of 
the  figures  themselves;  that  two  sets  of  figures  may  have  the 
same  average  yet  differ  among  themselves  in  a  striking 
manner.  It  is  often  important  to  find  out  what  these  differ- 
ences, or  variations,  are.  '  We  have  seen  that  one  way  to  do 
this  is  to  arrange  the  items  in  array,  that  is,  in  order  of 
magnitude  and  find  the  median,  the  mode,  the  quartiles  and 
so  on,  but  even  this  is  not  enough;  it  is  necessary,  if  possible, 
to  find  some  mathematical  relation  between  the  variations. 

Natural  frequency.  —  It  is  a  curious  and  important  fact 
that  if  we  measure  natural  objects,  such  as  the  lengths  of  the 
leaves  on  a  tree,  or  the  heights  of  a  regiment  of  men,  or  the 
lengths  and  breadths  of  nuts,  to  use  illustrations  studied  by 
the  Eldertons  in  their  Primer  of  Statistics,  we  shall  find  that 
most  of  the  observations  will  be  very  close  to  the  mean  of  all, 
that  a  few  will  differ  from  it  considerably  and  that  a  very 
small  number  will  differ  from  it  very  greatly.  In  a  thousand 
observations  a  certain  number  are  almost  sure  to  differ  from 
the  mean  by  a  definite  amount,  and  a  certain  other  number 
are  almost  sure  to  differ  from  the  mean  by  twice  that  amount. 
In  fact  these  relations  are  so  regular  as  to  amount  to  what 
may  be  called  a  law  of  nature,  a  sort  of  natural  frequency. 
In  these  variations  we  shall  find  some  observations  larger 
than  the  mean  and  some  smaller.  Natural  frequency  can 
best  be  understood  by  an  example. 

376 


NATURAL  FREQUENCY 


377 


In  a  certain  army  the  results  of  measurement  of  the 
heights  of  18,780  soldiers  were  as  follows: 


TABLE  131 
HEIGHTS  OF  SOLDIERS 


Height  in  inches. 

Number  of  soldiers. 

Per  cent  of  soldiers. 

(1) 

(2) 

(3) 

60  + 

197 

1.05 

61  + 

317 

1.69 

62  + 

692 

3.69 

63  + 

1,289 

6.86 

64  + 

1,961 

10.44 

65  + 

2,613 

13.91 

66  + 

2,974 

15.84 

67  + 

3,017 

16.07 

68  + 

2,287 

12.18 

69  + 

1,599 

8.52 

70  + 

878 

4.67 

71  + 

520 

2.77 

72  + 

262 

1.39 

73  + 

174 

0.92 

Total 

18,780 

100.00 

It  will  be  seen  that  the  mode,  the  most  commonly  observed 
height,  was  in  height-group  67+,  i.e.,  5  feet  7  inches  and  5  feet 
8  inches.  The  mean  was  67.24  inches.  If  we  should  at- 
tempt to  stand  these  18,780  in  array  we  should  have  an 
impossible  task.  We  might  try  it,  however,  and  obtain 
something  like  this: 

There  are  18,780  soldiers  in  all.  The  middle  one  would  be 
number  9390,  or  between  this  and  9391.  By  counting  up 
from  the  left  we  find  that  the  median  is  just  a  little  below  67 
inches.  There  are,  of  course,  differences  in  height  in  each 
group  and  with  care  we  could  get  the  median  exactly.  By 
taking  a  weighted  average,  as  described  in  the  second  chapter, 
we  could  get  the  mean.  But  just  now  we  are  interested  in 


378 


PROBABILITY 


the  variations.  We  can  plot  the  number  of  soldiers  by  height 
groups,  as  in  Fig.  55.  This  will  give  us  a  characteristic 
curve  highest  in  the  middle  and  sloping  downwards  gently 


o 
^noo  aoj; 


towards  either  end.  This  is  called  a  frequency  curve.  It 
should  be  noticed  that  whereas  in  the  array  the  height  was 
indicated  by  the  vertical  scale  it  is  in  this  diagram  indicated 
by  the  horizontal  scale. 


WHAT  IS  MEANT  BY   "CHANCE" 


379 


Coin  tossing.  —  Ten  coins  were  tossed  into  the  air  by  the 
students  in  one  of  my  classes  an  aggregate  of  1250  times, 
records  being  kept  of  the  number  of  heads  which  came  up. 
The  results  were  as  follows: 


TABLE   132 
RESULTS  OF  COIN  TOSSING 


Number  of  heads 
up  at  once. 

Number  of  throws. 

Number  of  heads 
up  at  once. 

Number  of  throws. 

(1) 

(2) 

(1) 

(2) 

0 

1 

6 

266 

1 

15 

7 

128 

2 

62 

8 

55 

3 

156 

9 

13 

4 

265 

10 

1 

5 

288 

These  results  when  plotted  gave  a  frequency  curve  which 
was  much  like  that  obtained  for  the  soldiers.  This  curve 
was  evidently  the  result  of  chance.  One  cannot  tell  for  any 
given  throw  how  many  heads  will  come  up,  yet  in  the  long 
run  we  always  get  some  such  result  as  that  obtained  by  the 
coin  tossing  students. 

What  is  meant  by  "  chance. " — What  determines 
whether  a  coin  thrown  into  the  air  will  fall  with  the  head  up  ? 
Many  things,  of  course,  —  the  way  it  is  held  when  thrown, 
the  twist  with  which  it  starts,  the  height  to  which  it  rises, 
the  manner  in  which  it  strikes  the  -floor,  the  way  it  rolls,  and 
many  other  factors.  The  sum  total  of  these  many  causes 
gives  what  we  call  "chance."  Chance  is  not  the  absence  of 
cause,  it  is  the  result  of  a  multiplicity  of  causes.  In  chance 
we  must  judge  the  result  by  the  combination  of  these  many 
causes.  Often  it  is  the  only  way  we  can  judge  the  result. 
In  chance  we  can  never  tell  exactly  any  particular  result, 


380  PROBABILITY 

but  we  can  form  an  idea  as  to  the  frequency  with  which  any 
possible  result  will  occur. 

In  the  case  of  the  coins  we  could  not  tell  in  advance  the 
result  of  any  particular  throw  of  ten  coins  but  we  could  safely 
predict  that  five  heads  would  be  thrown  more  often  than  any 
other  number,  and  that  no  heads  or  ten  heads  would  happen 
least  frequently.  Is  there  any  way  by  which  the  frequency 
that  other  numbers  of  heads  would  be  thrown  can  be  ascer- 
tained? There  is,  and  it  is  quite  simple. 

We  will  start  with  a  single  coin.  We  toss  it  up.  It  is  an 
even  chance  as  to  whether  it  comes  up  a  head  or  a  tail.  If 
we  should  toss  the  coin  a  hundred  times  we  would  probably 
have  a  head  in  fifty  of  the  throws.  In  practice  it  might  not 
come  out  exactly  50,  it  might  be  48  or  55,  but  if  we  tossed 
the  coin  an  enormously  large  number  of  times  a  head  would 
come  up  half  the  time.  Let  us  now  take  two  coins  which 
we  will  call  a  and  6.  If  we  indicate  a  head  by  heavy  type 
then  we  have  the  following  possible  combinations: 

ab;  ab;  ab;  ab. 

We  thus  have  the  following  results: 

Heads  012 

Number  of  throws         121  Total  4 

If  we  have  three  coins  we  have  the  following  possible 
chances : 

abc;  abc,  abc,  abc;  abc,  abc,  abc;  abc. 
Heads  0123 

Number  of  throws         1331  Total  8 

If  we  have  four  coins  we  have: 

abed;  abed,  abed,   abed,  abed;   abed,  abed,  abed,  abed, 
abed,  abed;  abed,  abed,  abed,  abed;  abed. 

Heads  01234 

Number  of  throws         14641        Total  16 


BINOMIAL  THEOREM 


381 


And  so  it  goes  on  until  for  10  coins  we  have: 

Heads  01234       56789  10 

Number  of  throws    1  10  45  120  210  252  210  120  45  10    1  Total  1024 

Theoretically,  therefore,  the  coins  in  1250  throws  should 
have  given  us  the  following  numbers:  These  compare  rea- 
sonably well  with  those  obtained  by  the  students. 


TABLE  133 
THEORETICAL  RESULT  OF  TOSSING   10  COINS  1260  TIMES 


Number  of  heads. 

Number  of  throws. 

Number  of  heads. 

Number  of  throws. 

(1) 

(2) 

(1) 

(2) 

0 

1 

6 

257 

1 

12 

7 

147 

2 

55 

8 

55 

3 

147 

9 

12 

4 

257 

10 

1 

5 

354 

Binomial  theorem.  —  Another  interesting  fact  is  that 
these  numbers  which  we  have  just  obtained  as  representing 
what  would  result  from  applying  the  laws  of  chance  to  the 
tossing  of  two,  three  and  more  coins,  are  the  same  as  are 
obtained  by  expanding  the  sum  of  two  quantities  by  the 
binomial  theorem,  (a  -\-  b)n  in  which  each  quantity,  a  and  b 
is  taken  as  1,  i.e.,  (1  +  l)n.  In  the  problem  a  head  was  just 
as  likely  to  come  up  as  a  tail.  In  this  expression  n  is  the 
number  of  coins.  If 

n  =  1,  (1  +  l)i  =  1  +  1, 

n  =  2,  (1  + I)2  =  1  +  2  +  1, 

n  =  3,  (1  +  I)3  =  1  +  3  +  3    +  1, 

n  =  4,  (1  +  I)4  =  1  +  4  +  6    +  4    +  1, 

n  =  5,  (1  +  I)5  =  1  +  5  +  10  +  10  +  5  +  1. 


382  PROBABILITY 

The  binomial  theorem,  therefore,  gives  us  a  method  of 
finding  the  shape  of  any  natural  frequency  curve  if  we  know 
the  number  of  terms.  It  should  be  observed  that  only  the 
even  values  of  n  give  an  odd  number  of  terms  with  a  middle 
highest  term. 

Some  interesting  conclusions  may  be  predicted  from  this 
application  of  the  binomial  theorem.  One  of  thein  is  that 
the  larger  the  number  of  terms  the  more  closely  are  the 
items  clustered  around  the  median  figure.  It  follows  that 
the  average  of  a  large  number  of  observations  is  much  more 
precise  than  the  average  of  only  a  few  observations.  In 
fact,  it  can  be  shown  that  the  error  of  a  set  of  observations 
varies  inversely  as  the  square  of  the  number  of  observations. 
If  we  multiply  the  number  of  observations  by  four,  we  halve 
the  probable  error. 

Chance  and  natural  phenomena.  —  Does  it  follow  there- 
fore that  the  measurements  of  natural  phenomena  result 
from  chance?  Certainly,  if  they  follow  the  binomial  law  as 
pointed  out.  How  is  it  in  the  case  of  the  heights  of  soldiers? 
Here  we  had  18,780  soldiers.  Theoretically,  these  should 
have  been  distributed  as  shown  in  Column  3.  Actually  they 
were  distributed  as  in  Column  2.  The  differences  are  very 
slight. 

What  are  the  many  causes  which  determine  a  person's 
height?  It  is  difficult  to  say.  Possibly  inheritance,  age, 
nationality,  food  supply  during  the  period  of  growth,  early 
illnesses,  habits  of  sleeping,  sitting,  standing  and  many  other 
factors.  It  would  be  an  interesting  subject  for  discussion. 
Whatever  the  causes  are  they  are  combined  in  so  many  ways 
that  we  have  no  better  method  of  predicting  the  heights  of 
the  soldiers  in  a  regiment  than  by  the  application  of  this 
law  of  chance. 


SKEW  CURVES 


383 


TABLE  134 
HEIGHTS  OF  SOLDIERS 


Per  cent  of  soldiers. 

Height  in  inches. 

Actual. 

Theoretical. 

(1) 

(2) 

(3) 

60  + 

1.05 

1.00 

61  + 

1.69 

1.71 

62  + 

3.69 

3.68 

63  + 

6.86 

6.75 

64  + 

10.44 

10.51 

65  + 

13.91 

13.99 

66  + 

15.84 

15.84 

67  + 

16.07 

15.31 

68  + 

12.18 

12,60 

69  + 

8.52 

8.84 

70  + 

4.67 

5.31 

71  + 

2.77 

2.67 

72  + 

1.39 

1.18 

-73  + 

0.92 

0.61 

100.00% 

100.00% 

Skew  curves.  —  In  plotting  natural  phenomena  it  will  be 
found  that  not  all  frequency  curves  are  symmetrical.  The 
median  is  not  always  the  mean;  there  may  be  more  items  on 
one  side  of  the  mean  than  on  the  other.  The  asymmetrical 
curves  are  known  as  skew  curves.  They  are  not  susceptible 
of  mathematical  analysis  except  by  the  use  of  complicated 
and  rather  uncertain  methods. 

There  are  four  common  types  of  asymmetrical  curves 
commonly  met  with  in  demographic  studies.  These  are 
shown  in  Fig.  56.  In  this  diagram  A  represents  the  sym- 
metrical frequency  curves,  the  two  sides  of  which  are  sym- 
metrical about  the  mode.  This  type  of  curve  has  already 
been  discussed.  Type  B  is  represented  by  the  age  distribu- 
tion of  deaths  from  measles.  In  early  childhood  the  curve 


384 


PROBABILITY 


rises  sharply.     Type  C  is  a  variant  of  B.     Type  D  starts  off 

with  the  mode  and  steadily 
diminishes.  Age  distribu- 
tion of  infant  deaths  by 
months  gives  us  an  example 
of  this  curve.  Type  E,  the 
U-shaped  curve,  is  already 
familiar  to  us.  It  is  sub- 
stantially the  curve  of  spe- 
cific death-rates  by  ages. 
All  of  these  skew  curves 
take  many  forms. 

It  will  be  remembered 
that  in  the  case  of  the  law  of 
chance  it  was  assumed  that 
the  chance  of  an  event 
happening  and  of  its  not 
happening  were  equal.  The 
chance  of  the  coin  falling 
as  a  head  was  the  same  as 
that  of  its  falling  as  a  tail, 
and  one  or  the  other  was 
bound  to  happen.  But  we 
can  imagine  a  result  de- 
pending upon  many  factors, 
one  of  which  was  much  more 
likely  to  occur  than  not  to 
occur.  This  would  result 
in  producing  a  skew  curve. 
There  might  be  many  such 
factors,  and  these  might  exist 
TYPE  E  u  -  SHAPED  m  au*  sorts  of  combinations. 
FIG.  56.  —  Types  of  Frequency  When  statistics  naturally 

Curves<  plot  out  as  a  skew  curve  it 


TYPE  D      J -SHAPED 


DEVIATION   FROM   THE  MEAN  385 

is  a  sign  that  they  should  be  investigated  to  determine,  if  pos- 
sible, what  the  influence  is  which  is  producing  the  skewness. 
Sometimes  it  can  be  found.  For  example,  in  a  case  recently 
studied  the  quantity  of  butter  fats  in  a  series  of  analyses 
of  milk  samples  was  slightly  skewed  at  one  end.  This  was 
found  to  be  due  to  the  adulteration  of  about  five  per  cent 
of  the  samples  with  water. 

Beyond  recognizing  the  skewness  of  a  curve  and  making 
some  attempt  to  account  for  it,  the  student  of  vital  statistics 
will  do  well  to  let  the  mathematics  of  skew  curves  alone. 
Karl  Pearson  and  others  of  his  school  have  suggested  certain 
methods  of  mathematical  analysis. 

Frequency  shown  by  summation  diagrams.  —  Another 
way  of  expressing  "frequency"  is  by  the  use  of  the  summa- 
tion, or  cumulative,  diagram.  In  some  respects  this  is  more 
useful  than  the  method  of  plotting  by  separate  groups.  Let 
us  return  to  our  18,780  soldiers  whose  heights  were  measured. 
If  197  soldiers  were  between  60"  and  61"  then  197  were 
less  than  61";  if  317  were  between  61"  and  62"  then  197  + 
317,  or  514,  were  less  than  62";  and  so  on.  If  these  results 
are  plotted  we  shall  obtain  a  characteristic  ogee  curve.  If 
the  distribution  is  exactly  in  accordance  with  the  law  of 
natural  frequency  then  the  upper  and  lower  parts  of  the 
curve  will  be  symmetrical. 

Instead  of  using  the  actual  numbers  of  soldiers  beginning 
with  197  and  running  up  to  18,780,  we  might  have  plotted 
the  percentage  distribution  from  1.05  per  cent  to  100  per  cent. 
The  result  would  have  been  the  same. 
•  Deviation  from  the  mean.  —  Still  another  way  of  study- 
ing these  figures  is  to  find  the  extent  to  which  the  heights  of 
the  soldiers  differed  from  the  average,  or  mean,  height.  The 
mean  height  was  67.24".  For  the  sake  of  simplicity  let  us 
call  it  67J".  We  may  fairly  assume  that  the  height  measure- 
ments were  measured  accurately  and  that  the  average  height 


386  PROBABILITY 

of  the  197  soldiers  in  height  group  60"  -  61"  was  60£". 
Then  the  average  deviation  of  the  height  of  these  197  soldiers 
from  the  mean  was  67  J  —  60£,  or  6J".  In  the  same  way  the 
317  soldiers  had  an  average  deviation  of  5J;  and  so  on. 
The  average  deviation  of  group  73  —  74"  was  73^  —  67J  or 
6J.  Some  of  these  deviations  are  positive  and  some  are 
negative,  because  some  of  the  soldiers  are  shorter  than  the 
mean  and  some  are  taller. 

If  we  plot  these  results  we  obtain  the  curve  shown  in 
Fig.  57.  This  is  the  curve  of  error,  so-called.  The  deviations 
from  the  mean  are  regarded  as  errors.  It  is  similar  to  the 
summation  curve  of  variation.  In  fact  it  is  the  same  curve, 
the  only  difference  being  the  scale.  Mathematicians,  physi- 
cists and  engineers  look  at  their  data  from  the  standpoint  of 
errors  of  observation,  and  therefore  their  text  books  which 
treat  of  this  subject  are  called  •"  Precision  of  Measurements, " 
"Theory  of  Least  Squares,"  and  the  like.  Natural  scientists 
however  speak  of  "  Variation."  It  is  all  one.  The  figures 
show  us  that  small  errors  occur  very  often,  large  errors  occur 
less  frequently,  and  very  large  errors  rarely  occur. 

In  any  set  of  measurements  we  may  assume  that  errors 
will  exist,  and  that  in  natural  phenomena  there  will  be  varia- 
tions caused  by  many  factors.  We  are  naturally  interested 
to  find  out  the  extent  of  these  variations.  We  want  to  know 
the  average  deviation  and  the  variation  most  likely  to  occur. 
It  will  not  be  possible  to  go  into  these  matters  in  great  detail 
in  this  book.  Readers  who  want  to  know  the  theory  of  these 
matters  must  study  the  theory  of  probability,  or  "Least 
Squares."  A  few  methods  of  dealing  with  the  subject 
practically  will  be  given  because  they  have  an  important  use 
even  in  elementary  statistics.  In  doing  so  we  will  consider 
first  a  very  simple  set  of  figures,  and  then  come  back  to  some 
more  measurements  of  men,  but  lest  we  tire  of  our  18,780 
soldiers  we  will  consider  some  more  recent  measurements 


STANDARD  DEVIATION 


387 


made  by  Drs.  Frankel  and  Dublin  of  the  Metropolitan  Life 
Insurance  Company. 

Standard  deviation.  —  Let  us  suppose  that  we  have  five 
figures,  or  statistics,  which  represent  something,  no  matter 


80 


100 


20  40  60 

Per  cent  of  Soldiers 

FIG.  57.  —  Percentage  Deviation  of  the  Heights  of  Soldiers  from 
the  Mean. 

what.  They  are  6,  8,  2,  4,  5.  The  mean  of  these  figures  is 
5.  The  deviations  from  the  mean  are  respectively  1,  3,  —3, 
—  1,  and  0.  The  average  deviation,  disregarding  signs,  is 


388 


PROBABILITY 


their  sum  divided  by  5,  or  1.6.  A  more  useful  quantity  is 
that  called  the  standard  deviation.  It  is  obtained  by  squaring 
these  deviations,  finding  the  average  square  and  taking  its 
square  root.  If  we  average  the  data  in  tabular  form  we  shall 
better  understand  the  process. 

TABLE   135 
STATISTICAL  DATA 


Item. 

Deviation  from 
Mean. 

Square  of 
Deviation. 

(1) 

(2) 

(3) 

6 

1 

1 

8 

3 

9 

2 

-3 

9 

4 

-1 

1 

5 

0 

0 

Sum  25 

81 

20 

Ave.   5 

1.6 

4 

1  Neglecting  signs. 

The  average  square  is  4  and  V4  is  2.  Hence  2  is  the  standard 
deviation.  It  will  be  noticed  that  the  standard  deviation 
gives  greater  weight  to  the  large  deviations  than  a  mere 
averaging  of  the  deviations  does. 

Coefficient  of  variation.  —  The  ratio  between  the  stand- 
ard variation  and  the  mean  is  called  the  coefficient  of  varia- 
tion. In  the  case  just  mentioned  it  is  2  -r-  5,  or  0.40.  The 
coefficient  of  variation  is  usually  expressed  decimally.  If 
the  variations  are  very  small  the  coefficient  of  variation  is 
small.  If  the  variations  are  large  the  coefficient  of  variation 
is  large.  In  some  parts  of  the  country  the  annual  rainfalls 
do  not  vary  much  from  year  to  year.  In  Massachusetts  the 
coefficient  of  variation  is  about  0.17.  In  other  parts  of  the 
country  there  are  great  fluctuations  from  year  to  year.  In 


COMPUTING  THE  COEFFICIENT  OF  VARIATION      389 

Arizona  the  coefficient  of  variation  is  0.50.  A  low  coefficient 
means,  in  general,  that  the  figures  are  more  dependable;  a 
high  coefficient  means  that  they  are  likely  to  be  untrust- 
worthy because  of  their  fluctuations.  This  coefficient  is 
very  useful  in  the  study  of  vital  statistics. 

Computing  the  coefficient  of  variation  when  data  are 
grouped.  —  This  is  likely  to  cause  trouble  to  the  beginner. 
It  is  necessary  to  use  care  or  mistakes  will  be  made.  Sup- 
pose we  have  the  following  items  divided  into  magnitude 
groups  between  0  and  5,  the  measurements  being  made  to 
the  nearest  tenth  as  shown  in  columns  (1)  and  (2). 


TABLE  136 
STATISTICAL  DATA 


Magnitude 
group. 

Number  in 
group. 

Average 
magnitude. 

Product. 

Deviation 
of  number 
in  group. 

Square  of 
deviation. 

Product. 

(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

(7) 

0-0.9 

6 

0.45 

2.70 

1.76 

3.10 

18.60 

1-1.9 

8 

1.45 

11.60 

0.76 

0.58 

4.64 

2-2.9 

2 

2.45 

4.90 

-0.24 

0.06 

0.12 

3-3.9 

4 

3.45 

13.80 

-1.24 

1.54 

6.16 

4r-4.9 

5 

4.45 

.22.25 

-2.24 

5.02 

25.10 

Total 

25 

55.25 

54.62 

Mean 

2.21 

2  18 

Here  we  first  find  the  average  magnitudes  of  the  numbers 
in  each  group,  column  (3).  By  multiplying  these  by  the 
number  of  items  in  each  group  and  dividing  by  the  number 
of  items  we  have  (4)  the  weighted  average,  or  the  mean  of  all 
the  items.  This  is  2.21.  Subtracting  the  figures  in  column 
(3)  from  2.21  we  have  the  group  deviations  in  column  (5). 
These  are  squared  (6)  and  then  multiplied  by  the  number  of 
items  in  each  group  (7) .  The  sum  of  the  squares  divided  by 
25  gives  the  average  square,  i.e.,  2.18  and  \/2.18  is  1.48,  the 


390  PROBABILITY 

standard  variation.  1.48  -r-  2.21  gives  0.67  the  coefficient 
of  variation.  Unthinking  students  sometimes  multiply  the 
figures  in  column  (5)  by  those  in  column  (2)  before  squaring. 
This  is  wrong.  It  is  the  deviations  which  are  squared.  The 
subsequent  process  is  merely  to  get  the  weighted  average  of 
the  squares. 

Probable  error.  —  Neither  the  average  deviation  from 
the  mean  nor  the  standard  deviation  is  the  one  most  likely 
to  occur.  It  is  the  median  deviation,  or  the  median  error, 
which  is  most  likely  to  occur.  It  can  be  shown  by  calculus 
that  when  observations  follow  the  normal  law  of  error,  or 
the.  normal  frequency  distribution,  i.e.,  the  binomial  dis- 
tribution, the  median  deviation  is  about  two-thirds  of  the 
standard  deviation.  To  be  exact,  the  figure  is  0.6745.  If 
we  let  r  stand  for  this  median  deviation,  this  probable  error, 
and  if  we  let  x  be  any  individual  error,  and  if  n  =  the  number 
of  observations,  then,  remembering  that  the  sign  2  means 
"the  sum  of,"  we  shall  see  that 

/y/v.2 

r  =  0.6745     —. 


This  is  merely  the  mathematical  way  of  stating  what  we 
have  just  done.  Sz2  means  the  sum  of  all  the  squares  of  the 

2x2  /Sx2 

deviations,  -  -  means  the  average  square,  and  y  —  means 

the  square  root  of  the  average  square,  i.e.,  the  standard 
deviation.  Where  does  0.6745  come  from?  If  we  take  the 
curve  of  error  (Fig.  57),  and  consider  the  side  to  the  left  of 
the  middle  ordinate,  it  will  be  possible  to  draw  a  vertical  line 
somewhere  to  the  left  (or  the  right)  of  the  middle  which  will 
divide  the  area  included  between  the  curve  and  the  base  line 
into  two  equal  parts.  The  height  of  the  ordinate  which  will 
do  this  is  0.6745  that  of  the  middle  ordinate. 


THE  PROBABILITY  SCALE  391 

This  probable  error  is  quite  useful  in  statistics.  One  use 
is  that  of  throwing  out  of  consideration  doubtful  observations. 

Doubtful  observations.  —  Scientists  make  a  distinction 
between  errors  and  mistakes.  Errors  are  supposed  to  fall 
within  the  limits  of  probability;  mistakes  are  supposed  to  be 
glaring,  erratic  observations  which  really  ought  to  be  left 
out  of  account,  or  at  least  not  included  when  the  average  is 
computed.  We  have  all  had  experiences  of  this  kind.  In 
a  daily  record  of  the  number  of  bacteria  in  a  filtered  water 
we  may  find  that  where  most  of  the  figures  are  less  than  25 
per  cubic  centimeter  there  is  one  which  exceeds  1000.  Shall 
we  include  this  in  the  average  for  the  month?  If  we  do  we 
unduly  raise  the  average  for  the  month  and  bring  discredit 
on  the  filter.  And  yet  there  may  be  no  reason  for  excluding 
it.  It  may  have  been  a  fact.  And  a  fact  is  not  to  be  dis- 
carded. 

The  theory  of  probability  gives  us  a  means  of  telling 
whether  it  should  be  included  in  the  average  or  not.  If  we 
know  the  probable  error  r,  as  above  described,  then  we  shall 

find  that  there  is  an  allowable  ratio  of  -  which  depends  upon 
the  number  of  observations.  If  we  had  only  three  obser- 

Af*  , 

vations  then  any  value  of  the  ratio  -  which  is  greater  than 
about  2  should  be  regarded  as  outside  the  probable  variations 
resulting  from  the  law  of  chance.  If  n  is  10  the  limit  of  - 

is  3;  if  n  =  30,  then  the  limit  of  -  is  3.5;  if  n  is  100,  the  limit 

is  4;  if  n  is  500,  the  limit  is  5,  and  so  on.  These  values  are 
merely  approximate. 

The  probability  scale.  —  This  ratio  of  -,  the  ratio  of  any 

error  to  the  mean,  or  most  probable  error,  is  useful  in  another 
way  because  on  the  basis  of  the  binomial  distribution  we  can 


392 


PROBABILITY 


compute  the  frequency  with  which  any  value  of  -  is  likely  to 

occur.     We  call  this  the  probability  of  its  occurrence. 

If  x  is  any  error  and  r  is  the  most  probable  error  then  when 

-  =  1  the  chances  are  even  that  the  error  will  be  x.  There 
r 

are  as  many  chances  that  the  error  will  be  larger  than  x  as 
that  it  will  be  smaller.  We  may  call  this  a  " fifty-fifty" 
chance,  and  we  may  write  the  probability  of  its  occurrence 

x 
as  J  or  0.5.     If  -  is  less  than  1  the  probability  that  any  error 

will  be  less  than  -  is  less,  and  if  -  is  greater  than  1  the  prob- 
ability that  any  error  will  be  less  than  -  is  greater.  In  fact 
we  shall  find  that  the  following  relations  hold : 


TABLE  137 
PROBABILITY 


X 

r 

Probability  that  any 

error  will  be  less  than    • 
r 

z 
r 

Probability  that  any 

error  will  be  less  than  -  • 
r 

(1) 

(2) 

(1) 

(2) 

0.0 

0.0000 

1.7 

0.7485 

0.1 

0.0538 

1.8 

0.7753 

0.2 

0.1073 

1.9 

0.8000 

0.3 

0.1603 

2.0 

0.8227 

0.4 

0.2127 

2.1 

0.8433 

0.5 

0.2641 

2.2 

0.8622 

0.6 

0.3143 

2.3 

0.8792 

0.7 

0.3632 

2.4 

0.8945 

0.8 

0.4105 

2.5 

0.9082 

0.9 

0.4562 

2.6 

0.9205 

.0 

0.5000 

2.7 

0.9314 

.1 

0.5419 

2.8 

0.9410 

.2 

0.5872 

2.9 

0.9495 

.3 

0.6194 

3.0 

0.9570 

.4 

0.6550 

4.0 

0.9930 

.5 

0.6883 

5.0 

0.9993 

.6 

0.7195 

00 

1.000 

PROBABILITY  PAPER 


393 


/v» 

If  we  compute  the  values  of  -  which  correspond  to  certain 
probabilities  we  have  the  following  approximate  figures: 


TABLE  138 
PROBABILITY 


Probability. 

X 

r 

Probability. 

X 

r 

(1) 

(2) 

(1) 

(2) 

0.01 

0.02 

0.80 

1.90 

0.02 

0.04 

0.90 

2.44 

0.03 

0.06 

0.95 

2.91 

0.05 

0.09 

0.98 

3.45 

0.10 

0.19 

0.99 

3.82 

0.20 

0.38 

0.999 

4.887 

0.30 

0.58 

0.9999 

5.783 

0.40 

0.77 

0.99999 

6.592 

0.50 

1.00 

0.999999 

7.258 

0.60 

1.25 

0.9999999 

7.967 

0.70 

1.54 

Probability  paper.  —  Until  recently  it  has  been  difficult 
to  use  the  theory  of  probability  in  statistical  work,  but  it  is 
now  easy.  In  1913,  my  partner,  Dr.  Allen  Hazen,  devised  a 
new  kind  of  plotting  paper.  The  percentage  scale  was  so 
spaced  that  any  set  of  figures  which  fqllow  the  natural  law 
of  probability  would  plot  out  not  as  an  ogee  curve,  but  as  a 
straight  line.  The  spacing  was  based  fundamentally  on  the 
preceding  figures,  but  it  was  necessary  to  take  account  of 
the  sign  of  the  error,  whether  positive  or  negative,  and  make 
allowance  for  this  in  designing  the  plotting  paper.  '  The 
50  per  cent,  or  median  line,  was  placed  in  the  middle  of  the 
percentage  scale.  The  other  relative  distances  were  as  fol- 
lows. The  figures  given  cover  only  one  side  of  the  50  per 
cent  line. 


394 


PROBABILITY 


TABLE  139 
DATA  FOR  PREPARING  PROBABILITY  PAPER 


Line. 

Relative  dis- 
tance. 

Line. 

Relative  dis- 
tance. 

Line. 

Relative  dis- 
tance. 

(1) 

.   (2) 

(1) 

(2) 

(D 

<tf 

Per  cent. 

Per  cent. 

Per  cent. 

50 

0.000 

17 

1.415 

0.8 

3.573 

48 

0.074 

16 

1.474 

0.7 

3.646 

46 

0.149 

15 

1.537 

0.6 

3.727 

44 

0.224 

14 

1.602 

0.5 

3.821 

42 

0.300 

13 

1.670 

0.4 

3.933 

40 

0.376 

12 

1.742 

0.3 

4.077 

38 

0.453 

11 

1.818 

0.2 

4.267 

36 

0.531 

10 

1.906 

0.1 

4.585 

34 

0.611 

9 

1.988 

0.09 

4.630 

32 

0.693 

8 

2.083 

0.08 

4.685 

30 

0.777 

7 

2.188 

0.07 

4.748 

•28 

0.864 

6 

2.305 

0.06 

4.817 

26 

0.954 

5 

2.439 

0.05 

4.900 

24 

1.047 

4 

2.596 

0.04 

5.000 

22 

1.145 

3 

2.789 

0.03 

5.120 

20 

1.248 

2 

3.045 

0.02 

5.290 

19 

1.302 

1 

3.450 

0.01 

5.550 

18 

1.357 

0.9 

3.507 

As  first  used  the  percentage  scale  was  used  horizontally,  as 
in  Fig.  63.  There  are  some  advantages  plotting  the  per- 
centages as  ordinates  as  in  Figs.  58,  59  and  60. 

In  the  latter  the  horizontal  scale  is  the  ordinary  arithmet- 
ical scale.  The  vertical  scale  may  be  labeled  from  0  to  100 
per  cent,  in  either  direction,  or  it  may  read  from  0  to  50  on 
either  side  of  the  median  line.  It  depends  upon  whether  we 
want  to  keep  the  positive  and  negative  errors  separate  or  add 
them  together  and  consider  their  magnitude  alone. 

A  few  examples  of  the  use  of  this  probability  paper  will 
now  be  given. 

For  a  more  complete  description  of  this  paper  the  reader 
is  referred  to  the  author 's  monograph  on  the  "  Element  of 
Chance  in  Sanitation."  1 

1  Jour.  Franklin  Institute,  July,  1916. 


PROBABILITY  PAPER 


395 


99.99 


55 


65  70 

Height  in  inches. 


FIG.  58.  —  Distribution  of  Soldiers  According  to  Height.     Plotted 
on  Arithmetic-Probability  Paper. 


PROBABILITY 


0.01 


14  Ifi  22 

Death  Rates  per  1000 


FIG.  59.  —  Death-rates  of  Massachusetts  Cities  and  Towns. 
Plotted  on  Arithmetic-Probability  Paper. 


PROBABILITY  PAPER 


77 


90  100  110 

Per  cent  of  Median . 

FIG.  60.  —  Percentage  Variation  of  Death-rates  of  Massachusetts 
Cities  and  Towns  for  Three  Different  Decades.  Plotted  on 
Arithmetic-Probability  Paper. 


398  PROBABILITY 

Examples  of  use  of  probability  paper.  —  Fig.  58  shows 
the  distribution  of  soldiers  according  to  height  plotted  on 
probability  paper.  This  is  based  on  the  observations  with 
which  we  have  already  become  familiar.  It  will  be  noticed 
that  instead  of  forming  the  usual  ogee  curve  the  points 
fall  on  a  straight  line. 

Fig.  59  shows  that  the  death-rates  for  Massachusetts 
cities  and  towns  also  plot  out  on  this  paper  as  a  straight 
line.  Fig.  60  shows  that  in  1900-10  the  death-rates 
throughout  the  state  have  been  more  uniform  than  in 
1860-70.  This  is  indicated  by  the  different  slope  of  the  lines. 

For  an  example  of  the  use  of  logarithmic  probability 
paper,  see  Fig.  63. 

Another  use  of  probability.  —  Bernoulli's  theorem  gives 
us  another  interesting  application  of  the  theory  of  probability. 

If  we  let  p  represent  the  frequency  of  an  event  happening 
and  q  the  frequency  of  its  not  happening,  then  obviously 
p  +  q  =  1.  Unless  this  fundamental  condition  holds,  the 
laws  of  probability  do  not  hold.  It  is  always  well  to  see  if 
there  are  any  other  factors  than  p  and  q. 

If  we  let  n  represent  the  number  of  cases  considered,  and 
€  the  mean  error,  then  Bernouilli  says,  e  =  Vnpq.  We  need 
not  stop  here  to  prove  this,  but  we  may  see  how  it  can  be 
used.  If  n  is  large  then  €  is  a  fair  measure  of  the  deviation 
from  the  standard  for  it  is  said  that  in  2  out  of  3  cases  the 
deviation  will  be  less  than  e;  in  19  out  of  20  cases  less  than 
2  e;  and  deviations  greater  than  4  e  are  very  rare. 

Let  us  suppose  that  in  a  population  of  10,000  the 
general  death-rate  was  15  per  1000,  i.e.,  150  deaths  in  all. 


Th,n  „.  10,000;    ,-JjL;    ,  -          ;   then 


=  V  10,000  X  ^  X  -^r  =  V147.75  =  12.15  deaths, 


THE  FREQUENCY  CURVE  AS  A  CONCEPTION  399 

or  1.2  per  1000.  A  fluctuation  of  this  amount  from  year 
to  year  would  not  be  outside  of  the  bounds  of  chance  phe- 
nomena. If  the  population  were  1,000,000  then  e  would  be 
VI.  4775  or  1.2  deaths  in  1,000,000  or  0.012  per  thousand. 

Other  criteria  than  Bernoulli's  have  been  suggested  for 
this  computation.  The  results  differ  considerably,  and  none 
of  the  methods  must  be  taken  as  mathematically  exact. 

Let  us  suppose  we  are  studying  an  epidemic  of  typhoid 
fever  in  which  all  the  cases,  120,  were  actually  caused  by  the 
public  water  supply.  The  population  was  50,000.  There 
were  two  milk  dealers:  A  served  40,000  persons;  B  served 
10,000  persons.  What  would  be  a  chance  distribution  of 
cans  among  these  two  dealers?  If  they  were  distributed 
uniformly  we  should  expect  to  find  among  A's  customers 

^TTT^K  of  120,  or  96;  and  among  B's  customers  -  '  n,,,  or  24. 

OU,UUU 


Now  what  is  a  reasonable  variation  from  these  figures?     In 
the  case  of  A, 


I 
=  \ 


1  20          4Q  880 
o.OOO  X  w       X  =  10  approximately. 


Therefore,  if  A  had  any  number  between  86  and  106  it  would 
be  within  the  bounds  of  chance.  •  If  he  had  116  cases  it 
might  be  a  suspicious  circumstance.  In  the  case  of  B, 


, \  /  i  ( 1 1  u  in  v  v 

C    —     %/     J-vJiVyvJVy     f\     m* r\    s\s\s\     '^ 


If,  therefore,  B  had  more  than  27  cases  it  would  be  suspicious. 
The  frequency  curve  as  a  conception.  —  The  frequency 
curve  is  something  far  beyond  a  statistical  tool.  Prop- 
erly conceived  it  stands  for  a  universal  principle.  Not  all 
the  leaves  of  a  tree  are  alike,  not  all  shells  are  alike,  sol- 
diers are  not  all  of  the  same  height  or  weight.  We  cannot 
well  compare  the  tallness  of  pine  trees  and  elm  trees  with- 


400  PROBABILITY 

out  resorting  to  the  frequency  curve.  One  man  may  say, 
"  The  elm  tree  is  the  taller;  I  have  seen  elms  taller  than 
pines."  Another  says,  "  That  is  nothing;  pine  trees  have 
a  greater  average  height."  But  the  first  man  is  not  con- 
vinced. He  goes  back  to  his  own  observation  and  insists 
that  he  has  seen  elms  taller  than  pines.  To  give  the  true 
picture  both  men  need  to  know  the  frequency  of  different 
heights  of  both  elms  and  pines. 

Are  young  women  as  good  scholars  as  young  men? 
Assuming  that  we  have  an  adequate  definition  of  what  is 
meant  by  a  good  scholar,  can  we  settle  the  question  by 
saying  that  we  have  seen  young  women  who  were  better 
scholars  than  young  men,  or  that  the  average  of  scholar- 
ship is  higher  among  men;  must  we  not  know  the  fre- 
quency with  which  we  find  good  scholars  and  poor  scholars 
among  both  men  and  women?  It  is  quite  conceivable 
that  among  women  we  have  greater  extremes  of  scholar- 
ship than  among  men,  or  vice  versa. 

Are  women  as  well  fitted  for  voting  as  are  men?  Suffra- 
gists point  to  drunken  sots  and  say,  "  We  are  better  fitted 
to  vote  than  they  are."  When  they  say  this  they  are  com- 
paring the  end  of  one  frequency  curve  with  the  middle  or 
the  upper  end  of  the  other.  Such  comparisons  are  utterly 
meaningless. 

Sometimes  we  need  to  make  comparisons  on  the  basis 
of  lower  limits,  sometimes  on  the  basis  of  upper  limits, 
sometimes  we  ought  to  compare  modes,  sometimes  medians, 
sometimes  averages,  sometimes  we  do  not  know  the  facts 
well  enough  to  make  comparisons  at  all:  but  through- 
out all  realms  of  thought  an  appreciation  of  the  funda- 
mental importance  of  the  frequency  curve  will  help  us  to 
reason  soundly  and  will  prevent  us  from  making  false 
comparisons, 

The  frequency  curve  contains  in  itself  the  element  of 


THE  FREQUENCY  CURVE  AS  A  CONCEPTION   401 

beauty.  Moons  wax  and  wane;  the  tide  rises  and  falls; 
the  flowers  of  spring  come,  first  a  few,  then  many;  and  they 
disappear  in  the  same  way,  a  few  lingering  into  summer. 
It  is  said  that  we  live  in  a  world  of  chance.  Nothing  is 
more  true.  We  live  in  a  world  where  many  causes  are 
acting  with  and  against  each  other.  We  live  in  a  world  of 
frequency  curves.  Artists  and  architects  recognize  this. 
The  ogee  curve  is  the  line  of  beauty. 

EXERCISES  AND   QUESTIONS 

1.  Find  data  for  and  plot  an  example  of  a  typical  symmetrical  fre- 
quency curve.     (Anthropometrical  measurements.) 

2.  Find  data  for  and  plot  an  asymmetrical  frequency  curve  (specific 
death-rates  for  scarlet  fever,  diphtheria,  etc.). 

3.  Describe  the  application  of  Bernouilli's  Theorem  to  the  chance 
distribution  of  cases  among  milk  customers?     [See  Am.  J.  P.  H.,  Apr., 
1912,  p.  296.] 

4.  Construct  a  model  to  illustrate  ihe  general  law  of  probability. 
[See  Rosenau's  Preventive  Medicine,  Chapter  on  Heredity  and  Eu- 
genics.] 

5.  Repeat  the  coin  tossing  experiment  described  in  this  chapter. 

6.  Find  the  height  of  50  males  (or  females)  above  eighteen  years  of 
age,  and  compute: 

a.   The  average  deviation  from  the  mean. 
6.   The  standard  deviation. 

c.  The  coefficient  of  deviation. 

d.  The  probable  error. 

7.  Plot  the  height  records  of  these  persons  on  "probability  paper." 

8.  Discuss  the  use  of  the  law  of  chance  in  public  health  studies. 
(Whipple,  Geo.  C.     The  Law  of  Chance  in  Sanitation,  Jour.  Franklin 
Institute,  July,  1916.) 

9.  Prepare  a  short  statistical  abstract  of  the  stature  of  recruits, 
U.  S.  A.,  1906-15.     [Hoffman,  Frederick  L.     Army  Anthropometry 
and  Medical  Rejection.     Newark.     Prudential  Press,  1918,] 


CHAPTER  XIII 
CORRELATION 

Correlation  is  the  word  by  which  the  statistician  describes 
the  correspondences  or  relations  between  series,  classes  or 
groups  of  data;  in  fact,  it  is  largely  for  the  study  of  these 
relationships  that  statistics  are  collected. 

Deaths  from  typhoid  fever  are  arranged  by  months  in 
order  to  ascertain  if  there  is  a  fixed  relation  between  the 
frequency  of  such  deaths  and  the  season  of  the  year;  or  they 
are  arranged  by  the  age,  occupation  or  place  of  residence  of 
the  decedants  in  order  to  learn  of  any  other  correspond- 
ences which  may  exist.  The  heights  and  weights  of  men, 
or  women,  are  compared  to  see  if  the  variations  in  height  are 
related  to  variations  in  weight;  the  length  of  the  arm  is 
compared  with  some  other  measurement  of  the  body;  the 
heights  of  sons  are  compared  with  the  heights  of  their  fathers. 
These  are  all  simple  correlations.  Two  sets  of  measurements 
only  are  compared. 

Often  the  problem  is  more  complicated.  The  infant 
mortality  in  cities  varies  with  the  season,  being  highest  in 
the  summer;  the  temperature  of  the  air  also  varies  with  the 
season,  being  highest  in  the  summer;  and  the  statistician 
desires  to  ascertain  if  there  is  any  definite  relation,  any 
correlation,  between  atmospheric  temperature  and  infant 
mortality.  Here  there  are  three  elements  to  be  considered  — 
season,  temperature  and  infant  mortality.  Also  the  number 
of  flies  ordinarily  increases  with  an  increased  atmospheric 
temperature,  and  the  question  arises  "Is  there  a  fixed  re- 

402 


CAUSAL  RELATIONS  403 

lation  between  the  increase  in  the  number  of  flies  and 
the  infant  mortality ?"  One  naturally  asks:  "Why  not 
eliminate  the  temperature  of  the  air  and  study  the  direct  and 
simple  correlation  between  flies  and  mortality?  That 
would,  indeed,  be  the  best  and  safest  method,  but  unfortu- 
nately the  data  may  not  exist,  or  cannot  be  obtained  in 
comparable  form.  It  is,  therefore,  necessary  to  devise  some 
way  of  studying  this  problem  by  indirect  correlation,  or 
secondary  correlation. 

Causal  relations.  —  Sometimes  statistics  are  studied 
merely  to  determine  whether  correlation  exists  between  two 
variables,  this  result  being  practically  useful.  The  knowledge 
that  infant  mortality  increases  with  the  atmospheric  tem- 
perature is  in  itself  of  value  to  the  physician  and  the  health 
officer.  More  often  perhaps  the  underlying  motive  in  corre- 
lation studies  is  that  of  determining  cause  and  effect.  In 
the  illustration  given  the  question  is,  Is  the  increase  in 
atmospheric  temperature  the  cause  of  the  increased  mor- 
tality among  infants?  Is  the  increase  in  the  number  of  flies 
in  the  summer  the  cause  of  the  increased  infant  mortality? 
Or,  to  go  back  to  the  examples  of  simple  correlation,  Is  the 
increased  height  of  men  the  cause  of  their  increased  weight? 
Is  the  tallness  of  a  son  the  effect  of  the  tallness  of  his  father  ? 
Does  the  establishment  of  correlation  also  mean  that  a 
causal  relation  has  been  established?  To  answer  this  we 
must  consider  what  is  meant  by  cause. 

Jevons  l  says:  "By  the  cause  of  an  event  we  mean  the 
circumstances  which  must  have  preceded  in  Border  that  the  event 
should  happen.  It  is  not  generally  possible  to  say  that  an 
event  has  one  single  cause  and  no  more.  The  cause  of  the 
loud  explosion  in  a  gun  is  not  simply  the  pulling  of  the  trigger, 
which  is  only  the  last  apparent  cause  or  the  occasion  of  the 
explosion;  the  qualities  of  the  powder,  the  proper  form  of 
1  Lessons  in  Logic,  p.  239. 


404  CORRELATION 

the  barrel;  the  existence  of  some  resisting  charge;  the  proper 
arranging  of  the  percussion  cap  and  powder;  the  existence 
of  a  surrounding  atmosphere,  are  among  the  circumstances 
necessary  to  the  loud  report  of  the  gun;  any  of  them  being 
absent  it  would  not  have  occurred."  In  the  above  phrase, 
"the  circumstances  which  must  have  preceded  in  order  that 
the  event  should  happen,"  emphasis  must  be  placed  on  the 
word  must,  otherwise  our  reasoning  is  post  hoc  non  propter 
hoc. 

[  It  is  obvious  that  statistics  do  not  in  themselves  establish 
these  causal  relations.  The  laws  of  logic  are  the  primary 
laws,  and  the  rules  of  statistics  must  be  subsidiary  to  them. 
Westergaard,  the  celebrated  Danish  statistician,  has  recently 
said  (Jour.  Am.  Stat.  Asso.,  Sept.  1916,  p.  259),  "that  the 
task  of  the  statistician  is  not  so  much  to  find  the  causality 
himself  as  to  help  others  to  find  it.  The  statistician  must  be 
content  if  he  can  show  that  certain  groups  of  numbers  have 
marked/lifferences,  leaving  it  to  physiology,  meteorology  arid 
other  sciences  to  explain  these  differences." 

The  statistician  can  prove  nothing  by  his  statistics  unless 
he  uses  them  logically. 

On  the  other  hand,  the  statistical  arrangements  of  facts 
are  of  the  greatest  aid  in  helping  to  establish  causal  relations, 
because  by  expressing  facts  by  numbers  it  is  possible  to  con- 
centrate extended  experiences  into  quantities  which  may  be 
easily  and  quickly  compared. 

Correlation  and  causality.  —  In  studying  correlation  as 
a  process  for  determining  causality  it  is  necessary  to  dis- 
tinguish between  the  simple  correlation  which  may  exist 
between  two  variables  and  the  more  indirect  correlation,  or 
secondary  correlation,  which  occurs  when  two  series  of  events, 
both  correlated  to  a  third  factor,  are  compared  to  each  other. 
The  former  may  be  safely  used  to  establish  a  causal  relation; 
in  fact,  King  says  (Elements  of  Statistics,  p.  197),  that 


LAWS  OF  CAUSATION  405 

"correlation  means  that  between  two  series  or  groups  of 
data  there  exists  some  causal  relation."  In  stating  this  he 
evidently  had  in  mind  the  simple  correlation  between  two 
variables.  And,  of  course* " causal  relation"  does  not  mean 
"sole  cause."  Besides  correlation  we  must  also  establish 
connection  between  the  two  variables.  It  is  not  the  task  of 
the  statistician  to  do  this.  It  would  be  more  exact  to  say 
that  a  causal  relation  may  be  shown  by  establishing  a  definite 
correlation  between  two  series,  classes  or  groups  of  connected 
data. 

It  is  chiefly  in  secondary  correlations  that  we  err  in  our 
logical  processes.  In  mathematics  we  learned  that  "two 
things  which  are  equal  to  a  third  are  equal  to  each  other," 
but  it  is  not  necessarily  true  that  two  series  of  events  which 
vary  as  a  third  are  equal  to  each  other,  or  even  are  related  to 
each  other  at  all.  Infant  mortality  increases  with  the 
atmospheric  temperature  in  summer;  the  softness  of  the 
asphalt  pavements  increases  with  the  atmospheric  tempera- 
ture in  summer;  but  we  cannot  infer  that  there  is  any 
relation  between  infant  mortality  and  the  softness  of  asphalt 
pavements. 

The  actual  connection  between  events  is  not  shown  by 
statistics  or  by  the  statistical  methods  except  as  the  data  are 
interpreted  according  to  the  laws  of  logic. 

Let  the  reader  try  to  answer  questions  like  these.  Why 
is  it  not  true  that  there  is  a  causal  relation  between. the  soft- 
ness of  pavements  and  infant  mortality?  Is  it,  or  is  it  not, 
true  that  there  is  a  causal  relation  between  the  presence  of 
flies  and  infant  mortality?  Which  shows  the  higher  degree 
of  correlation  with  infant  mortality  —  the  presence  of  flies 
or  the  softness  of  asphalt  ? 

Laws  of  causation.  —  While  we  are  thinking  about  cor- 
relation and  its  relation  to  causation  it  will  not  be  out  of 
place  to  refer  to  the  three  methods  of  induction  as  stated 


406  CORRELATION 

by  John  Stuart  Mill.  The  cause  of  an  event  may  be  said 
to  be  "the  circumstances  which  must  have  preceded  in 
order  that  the  event  should  happen." 

Mill's  first  canon  is,  "  If  two.  or  more  instances  of  the 
phenomenon  under  investigation  have  only  one  circum- 
stance in  common,  the  circumstance  in  which  alone  all  the 
instances  agree  is  the  cause  (or  effect)  of  the  given  phe- 
nomenon." This  is  the  method  of  agreement.  The  epi- 
demiologist follows  this  principle  when  he  studies  case 
after  case  of  disease  looking  for  some  common  antecedent 
circumstance.  Here  one  instance  does  not  establish  proof 
of  a  cause,  and  the  larger  the  number  of  instances  the 
stronger  the  proof. 

The  second  canon  is  "if  an  instance  in  which  the  phe- 
nomenon under  investigation  occurs,  and  an  instance  in 
which  it  does  not  occur,  have  every  circumstance  in  com- 
mon save  one,  that  one  occurring  only  in  the  former;  the 
circumstances  in  which  alone  the  two  instances  differ  is 
the  effect,  or  the  cause,  or  an  indispensable  part  of  the 
cause,  of  the  phenomenon.  This  is  the  method  of  differ- 
ence, the  method  of  experiment.  This  principle  also  is 
used  in  epidemiology. 

The  third  canon  is  called  the  joint  method.  "  If  two  or 
more  instances  in  which  the  phenomenon  occurs  have  only 
one  circumstance  in  common,  while  two  or  more  instances 
in  which  it  does  not  occur  have  nothing  in  common  save 
the  absence  of  that  circumstance;  the  circumstance  in 
which  alone  the  two  sets  of  instances  (always  or  invariably) 
differ,  is  the  effect,  or  the  cause  or  an  indispensable  part 
of  the  cause,  of  the  phenomenon." 

These  are  sometimes  expressed  as  follows,  the  large  let- 
ters, A,  B,  C,  etc.,  representing  antecedents,  and  the  small 
letters,  a,  b,  c,  etc.,  the  consequents. 


METHODS  OF  CORRELATION  407 

Method  of  Agreement 

ABC  ab  c 

A  D  E  ade 

AF  G  af  g 

A  H  K  ahk 

Method  of  Difference 

ABC  ab  c 

B  C  be 

Joint  Method 

ABC  ab  c 

AD  E  ade 

AF  G  af  g 

AHK  ahk 

P  Q  pq 

R  S  r  s 

TV  t  v 

XY  xy 


Methods  of  correlation.  —  Correlations  may  be  divided 
into  two  classes :  —  (1)  simple,  or  primary,  and  (2)  secondary. 

Simple  correlations  are  studied  as  between  two  variables, 
these  two  variables  being  compared  on  the  basis  of  magni- 
tude, that  is  they  are  compared  by  grouping. 

Secondary  correlations  are  studied  when  two  variables  are 
compared  with  each  other  after  first  being  compared  to  a 
third  variable  —  such  as  time  or  place. 

When  two  variables  are  so  correlated  that  the  numerical 
values  increase  and  decrease  together  the  correlation  is  said 
to  be  direct. 


408  CORRELATION 

When  the  correlation  is  such  that  the  numerical  value  of 
one  variable  increases  as  that  of  the  other  decreases  the, 
correlation  is  said  to  be  inverse. 

The  closeness  of  correlation  is  termed  the  degree  of  correlation. 
There  are  mathematical  methods  of  determining  the  degree 
of  correlation,  according  to  which  perfect  correlation  is  repre- 
sented by  unity  and  complete  absence  of  correlation  by  zero. 

The  following  are  some  of  the  methods  used  in  the  study 
of  correlation: 

Simple  correlations  (two  variables  compared  directly) : 

1.  Plotting  of  original  data. 

2.  Correlation  table  (grouping  by  lines  and  columns), 

3.  Correlation  model  (correlation  surface). 

4.  Plotting  of  group  means  (Galton). 

5.  Computation  of  coefficient  of  correlation: 

(a)   Galton's   method    (see   Elderton's    Primer   of 

Statistics). 
(6)   Karl  Pearson's  method. 

6.  Use  of  mathematical  formulae. 

Secondary  correlations  (two  variables  compared  on  the 
basis  of  a  third  variable) : 

1.  Comparisons  between  two  plotted  lines  representing 

original  data,  as  to: 

(a)  Parallelism. 

(b)  Correspondence  of  fluctuation  in  time  of  oc- 

currence and  in  magnitude. 

(c)  Correspondence  of  cycles. 

(d)  Lag. 

(e)  Inverse  relations. 

2.  Comparison  between  two  plotted  lines,  each  represent- 
ing variations  from  the  mean. 

3.  Comparison  between  two  plotted  lines,  each  represent- 
ing variations  from  the  moving  average  (or  some  smoothed 
line  showing  trend). 


GALTON'S  COEFFICIENT  OF  CORRELATION       409 


Gallon's  coefficient  of  correlation.  —  Let  us  suppose  that 
we  have  the  following  pairs  of  observations.  Each  a  has  a 
corresponding  b.  What  is  the  correlation  between  a  and  6? 
Offhand  one  can  see  that  in  a  general  way  a  and  b  rise  and 
fall  together.  But  how  can  we  express  this  relation? 

TABLE  140 
EXAMPLE  OF  CORRELATION 


a 

6 

X 

Z2 

V 

v- 

iy 

(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

(7) 

7 

4 

1 

1 

0 

0 

0 

5 

2 

-1 

1 

-2 

4 

2 

6 

5 

0 

0 

1 

1 

0 

3 

1 

-3 

9 

-3 

9 

9 

9 

8 

3 

9 

4 

16 

12 

Sum         30 

20 

20 

30 

23 

Average    6 

4 

4 

6 

4.6 

<T                        ... 

2 

2.45 

We  cannot  compare  the  figures  directly.  We  do  not  even 
know  that  the  measurements  are  the  same,  a  may  be 
expressed  in  feet,  and  b  may  mean  years  or  something  else. 
What  have  these  two  sets  of  figures  in  common?  The 
deviations  from  their  means  may  help  us.  Let  us  suppose 
that  x  represents  the  deviation  of  a  from  its  mean,  6,  and 
that  y  stands  for  the  deviations  of  b  from  its  mean,  4. 
Then  we  can  compute  the  standard  deviation  of  each  set 
of  figures,  and  call  these  ax  and  o-y.  These  we  find  to  be 
V4,  or  2,  and  A/6,  or  2.45.  We  must  now  link  together  the 
two  sets  of  observations  and  we  do  this  by  finding  the  prod- 
ucts of  their  deviations,  i.e.,  xy,  and  the  average  of  xy,  i.e., 
4.6.  This  average  value  of  the  product  of  x  and  y,  divided 
by  the  product  of  the  standard  variations,  ax  and  crv,  gives 
what  Galton  calls  the  coefficient  of  variation.  It  may  be 
expressed  by  formula  thus: 


410 


CORRELATION 


Coefficient  of  correlation  = 


,  in  which  n  is  the  num- 


ber of  observations,  and  2xy  the  sum  of  ah1  the  xy's.    In  the 


example, 


2xy      23 


—  =  4.6,  and  the  coefficient  is 


4.6 


n  b  2  X  2.45 

=  0.94.  This  is  a  close  correlation  between  a  and  6,  because 
1  represents  perfect  correlation  and  0  no  correlation  at  all. 

Pearson's  coefficient  is  not  quite  the  same,  but  it  is  enough 
for  practical  purpose  to  remember  Galton's. 

Example  of  low  correlation.  —  In  the  monthly  bulletin 
of  the  Connecticut  State  Department  of  Health  for  Feb., 
1918,  a  radial  diagram  is  given  showing  that  grippe  out- 
breaks in  one  year  are  followed  by  measles  the  next  year, 
and  the  statement  is  made  that  "  the  wheel  of  chance  becomes 
a  wheel  of  certainty."  Let  us  see  if  these  facts  will  stand 
the  test  of  correlation.  If  we  place  the  deaths  from  grippe 
in  one  year  side  by  side  with  the  deaths  from  measles  the 
following  year,  we  have  the  following  twelve  pairs  of  values 

for  a  and  b. 

TABLE  141 


b 

X 

z2 

V 

V2 

xy 

u) 

(2) 

(3) 

(4) 

(5) 

(6) 

(7) 

8 

32 

-2.25 

5.06 

16.92 

286.29 

-38.07 

4 

8 

-6.25 

39.06 

-  7.08 

50.13 

+44.25 

15 

26 

4.75 

22.56 

-  9.08 

82.45 

-43.13 

11 

5 

0.75 

0.56 

9.92 

98.41 

+  7.44 

6 

6 

-4.25 

18.06 

-  9.08 

82.45 

+38.59 

8 

22 

-2.25 

5.06 

-13.08 

171.09 

+29.43 

16 

0 

5.75 

28.06 

4.92 

24.21 

+28.29 

7 

3 

-3.25 

33.06 

-12.08 

145.93 

+39.26 

12 

27 

1.75 

3.06 

11.92 

142.09 

+20.86 

2 

12 

-8.25 

68.06 

-  3.08 

9.49 

+25.41 

9 

6 

-1.25 

1.56 

-  9.08 

82.45 

+  11.35 

25 

34 

14.75 

217.56 

18.92 

357.97 

+279.07 

Sum        123 

181 

441  72 

1532  96 

442  75 

Average  10.25 

15.08 

36.81 

127.75 

6  07 

11  30 

CORRELATION  SHOWN  GRAPHICALLY  411 

It  will  be  seen  that  the  coefficient  of  correlation  is 

442.75 


12X6.07X11.30 


This  is  a  low  correlation.  It  is  less  than  the  coefficient  of 
variation  of  either  grippe  or  measles.  It  follows,  therefore, 
that  the  statement  that  grippe  is  followed  by  measles  a  year 
later  has  little  to  substantiate  it,  if  all  the  facts  are  considered. 
If  we  leave  out  a  few  exceptional  years  there  does  appear  to 
be  a  general  tendency  for  measles  to  follow  grippe.  But 
what  right  is  there  to  leave  out  some  of  the  facts?  If  they 
are  mistakes  they  should  be  left  out,  otherwise  they  should 
be  considered  in  drawing  concessions. 

A  few  years  ago  a  sanitary  chemist  tried  to  show  a  relation 
between  the  color  of  water  and  the  typhoid  fever  death-rates 
in  Massachusetts  water  supplies.  Computations  of  the 
coefficient  of  correlation  for  54  places  where  surface  water 
was  used  gave  a  figure  of  0.16,  while  for  33  places  where 
ground  water  was  used  it  was  0.30.  In  other  words  there 
was  very  little  correlation.  In  the  same  cities  the  correla- 
tions between  the  general  death-rates  and  the  typhoid  fever 
death-rates  were  0.59  and  0.56,  respectively. 

On  the  other  hand,  the  Eldertons  found  the  coefficient  of 
correlation  between  the  length  and  breadth  of  shells  to  be 
0.95;  that  between  the  ages  of  husbands  and  wives,  0.91. 

The  student  will  find  the  use  of  the  coefficient  of  correlation 
an  admirable  weapon  for  exploding  false  theories. 

Correlation  shown  graphically.  —  In  a  general  sense  any 
graph  with  horizontal  and  vertical  scales,  in  which  pairs  of 
observations  are  represented  by  a  single  point  is  a  correlation 
plot.  If  the  points  fall  on  or  near  a  straight  line  the  correla- 
tion is  high;  if  the  points  are  so  scattered  that  a  straight  line 
cannot  be  readily  drawn  to  represent  them  the  correlation 
is  low.  This  needs  no  further  illustration. 


412 


CORRELATION 


It  is  possible,  however,  to  determine  the  coefficient  of 
correlation  graphically.  In  Bowley's  Elements  of  Statistics 
we  find  the  relation  between  the  marriage-rate  and  the  price 
of  wheat.  The  first  step  is  to  select  two  suitable  scales  and 
plot  the  data  as  points.  The  second  step  is  to  find  the  mean 
marriage-rate  and  the  mean  price  of  wheat  and  plot  these  as 


17.0 


16.5 


16.0 


15.0 


14.5 


14.0 


:: 


30  40  50 

Price  of  Wheat,  in  Shillings 


60 


FIG.  61.  —  Correlation  between  Marriage-rate  and  Price  of  Wheat. 

horizontal  and  vertical  lines,  respectively.  The  third  step 
is  to  draw  a  line  which  will  fairly  well  represent  the  points. 
In  Fig.  61  this  line  is  marked  MN.  It  must  pass  through 
the  intersection  of  the  mean  lines,  0.  The  fourth  step  is  to 
select  any  point  on  MN,  as,  for  example,  A,  and  read  from 
the  vertical  scale  the  value  of  AB.  In  the  example  AB*  is 
16.7  -  15.17  =  1.53.  This  is  really  the  deviation  of  A 


THE  CORRELATION  TABLE  413 

from  the  mean  marriage-rate  and  1.53  -s-  15.17  =  10.15  is 
the  standard  variation.  In  the  same  way  AC  is  46.0  —  37.8 
=  8.2,  the  deviation  of  A  from  the  mean  price  of  wheat,  and 
8.2  -r-  37.8  =  21.7  is  the  standard  variation.  The  ratio  of 
10.15  to  21.7  gives  us  the  coefficient  of  correlation,  10.15  -5- 
21.7  =  0.468.  By  computation  Bowley  finds  this  to  be 
0.47.  The  graphical  method  is  useful  only  when  the  correla- 
tion is  fairly  high,  because  if  the  correlation  is  low  one  cannot 
tell  where  to  draw  the  line  MN.  In  drawing  this  line  an 
effort  should  be  made  to  place  it  so  that  there  will  be  as  many 
points  as  possible  near  the  line,  with  the  other  points  as  well 
balanced  as  possible  on  either  side  of  the  line.  This  requires 
experience  and  a  sort  of  intuitive  sense  of  distances. 

A  recent  example  of  lack  of  correlation.  —  The  Munic- 
ipal Tuberculosis  Sanitarium  of  Chicago,  in  its  annual 
report  for  1917,  has  published  an  interesting  series  of 
diagrams  illustrative  of  the  lack  of  correlation  between 
housing  and  tuberculosis.  Fig.  62  is  one  of  these.  The 
districts  are  arranged  in  order  of  occurrence  of  tubercu- 
losis. The  one-scale  rectangles,  appropriately  divided  ac- 
cording to  the  character  of  rooms,  fail  to  show  any  progres- 
sion coincident  with  tuberculosis  under  Chicago  conditions. 

The  correlation  table.  —  The  correlation  table  is  arranged 
much  like  a  simple  plot.  There  is  a  horizontal  and  a  vertical 
arrangement  of  groups.  This  tabulation  shows  to  the  eye 
the  relation  between  the  two  quantities.  In  Table  142  we 
see  the  correlation  between  the  ages  of  husband  and  wife  is 
fairly  close.  Of  669  wives  in  age-group  40-44, 309  were  married 
to  husbands  in  the  same  age-group.  There  is  a  slight  tend- 
ency for  husbands  to  be  slightly  older  than  their  wives.  The 
figures  are  not  symmetrically  arranged  around  the  mode. 

The  correlation  model  is  used  but  little.  A  description  of 
its  construction  and  use  may  be  found  in  works  on  statistical 
methods. 


414 


CORRELATION 


FIG.  62.  —  Diagram  Showing  Lack  of  Correlation  between  Interior 
Rooms  in  Certain  Chicago  Blocks  and  Tuberculosis  Morbidity. 


SECONDARY  CORRELATION 


415 


TABLE   142 

CORRELATION  BETWEEN  (1)  THE  AGE  OF  WIFE,  (2)  THE 
AGE  OF  HUSBAND,  FOR  ALL  HUSBANDS  AND  WIVES 
IN  ENGLAND  AND  WALES  WHO  WERE  RESIDING  TO- 
GETHER ON  THE  NIGHT  OF  THE  CENSUS,  1901. 
(CENSUS,  1901,  SUMMARY  TABLES,  P.  182.)  TABLE  BASED 
ON  6,317,620  PAIRS;  CONDENSED  BY  OMITTING  OOO'S 

(From  Yule's  Theory  of  Statistics,  p.  169.) 


A»T 

hus- 
bands. 

Ages  of  wives. 

Total. 

15- 

20- 

25- 

30- 

35- 

40- 

45- 

50- 

55- 

60- 

65- 

70- 

75- 

80- 

85- 

(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

(7) 

(8) 

(9) 

(10 

(11) 

(12) 

(13) 

(14) 

(15) 

(16) 

(17) 

15- 
20- 
25- 
30- 

2 
16 
4 
1 

2 
173 
185 
41 

4 
240 
688 
817 

46 
402 
265 

4 
84 
411 

10 

84 

2 
12 

1 

2 

35- 

9 

69 

251 

369 

80 

12 

2 

1 

793 

40- 
45- 
50- 
55- 
60- 
65- 

3 

1 

17 
6 
2 

1 

71 
20 
8 
3 

219 
66 
19 
8 
3 
1 

309 
178 
57 
18 
8 
3 

66 
252 
146 
46 
16 
6 

12 

59 
195 
110 
39 
11 

2 
10 
44 
141 
81 
26 

1 
2 
10 
35 
101 
53 

1 
2 
6 
23 
58 

1 
4 
13 

700 
595 
483 
369 
277 
175 

1 
2 

1 

70- 

1 

1 

2 

5 

8 

18 

31 

31 

6 

1 

104- 

75- 
80- 
85- 

1 

1 

2 
1 

3 
•1 

5 

1 

10 

2 

1 

14 
4 

1 

12 
5 

2 
3 
1 

~8~ 

1 

50 
18 
4 

Total 

23 

414 

808 

854 

781 

669 

550 

437 

317 

226 

134 

68 

27 

1 

5317 

Use  of  mathematical  formulae.  —  It  is  often  desirable  to 
find  the  equation  of  a  straight  line  or  curve  drawn  through 
a  series  of  points.  This  is  not  difficult,  but  it  requires  a 
longer  description  than  can  be  given  here.  The  student 
can  find  good  descriptions  of  the  methods  used  in  standard 
mathematical  books. 

Secondary  correlation.  —  The  correlation  of  two  variables 
is  often  shown  by  plotting  each  against  a  third  quantity, 
which  latter  varies  in  a  regular  manner.  Thus  in  Fig.  52  we 


416  CORRELATION 

have  the  number  of  cases  of  typhoid  fever  plotted  as  ordi- 
nates  with  months  as  abscissae,  and  we  have  also  the  atmos- 
pheric temperature  plotted  as  ordinates  with  months  as 
abscissae.  Here  we  see  that  there  is  a  general  correspondence 
between  the  two  curves  and  we  say  that  there  is  correlation 
between  the  two.  One  must  be  very  careful  in  using  the 
graphic  method  in  this  way.  We  may  have  a  diagram  in 
which  the  correspondence  between  the  two  plotted  lines  is 
very  definite  except  occasionally,  yet  these  occasional  lapses 
may  be  enough  to  upset  the  correlation.  Again  two  lines 
may  rise  and  fall  together  in  point  of  time,  and  they 
may  even  rise  and  fall  apparently  the  same  amounts,  yet 
this  may  be  an  incident  depending  on  the  scales  used. 
Finally  we  must  not  forget  that  this  sort  of  correlation  - 
where  two  quantities  vary  as  a  third  —  does  not  establish 
causality. 

In  Fig.  53  we  have  typhoid  fever  death-rates  and  popu- 
lation supplied  with  filtered  \vater,  both  plotted  with  time 
as  the  abscissae;  and  we  notice  that  as  one  line  goes  up 
the  other  goes  down,  giving  a  sort  of  inverse  correspond- 
ence. We  are  not  justified  however  in  calling  this  a 
close  correlation.  Certainly  we  are  not  justified  in  saying 
that  one  is  the  cause  of  the  other.  It  may  be  true,  and 
few  will  dispute  the  fact  that  the  filtration  of  polluted 
water  tends  to  reduce  the  typhoid  fever  death-rate  among 
the  consumers  of  the  water,  but  such  a  diagram  as  this 
does  not  prove  it.  As  Phelps1  says,  we  might  plot]  a  line 
showing  the  increase  in  the  number  of  telephones  which 
would  very  much  resemble  that  of  the  population  supplied 
with  filtered  water.  Pearson  does  well  to  call  this  correla- 
tion based  on  comparison  with  a  "common  mutual,"  a 
"  spurious  correlation."  A  good  many  false  conclusions 
have  been  based  on  statistics  treated  in  this  way. 
1  Am.  Jour.  Pub.  Health,  1917,  p.  23. 


THE  LAG  417 

The  lag.  —  When  two  lines  are  plotted  with  the  scale  of 
abscissae  in  common  to  both  variables  it  often  happens 
that  one  line  changes  in  curvature  after  the  other;  it  lags 
behind  it.  Sometimes  this  lag  is  very  regular,  sometimes 
it  is  more  or  less  irregular.  This  lag  does  not  necessarily, 
show  lack  of  correlation.  It  may,  on  the  other  hand,  result 
from  cause  and  effect.  It  is  obvious  that  a  cause  must 
precede  in  time  the  effect  produced  by  that  cause.  It  may 
require  a  certain  interval  of  time  for  the  cause  to  make 
itself  felt,  and  this  naturally  would  produce  a  lag.  For 
example,  let  us  suppose  that  it  takes  ten  days  after  a 
typhoid  infection  for  the  victim  to  "  come  down  "  with  the 
disease;  then  a  plotted  line  showing  by  days  the  number 
of  cases  of  typhoid  fever  would  lag  behind  a  line  showing 
infection  of  the  water-supply,  —  if  we  can  imagine  such 
facts  to  be  plotted.  Conversely,  if  we  had  the  two  plotted 
lines  we  might  compute  the  length  of  the  incubation  period 
of  typhoid  fever  by  measuring  the  lag.  If  the  comparison 
is  between  the  dates  of  infection  and  the  dates  of  deaths 
from  typhoid  fever,  then,  of  course,  the  lag  is  much  longer 
as  it  includes  not  only  the  period  of  incubation,  but  also 
the  run  of  the  disease,  and  this  is  not  the  same  for  all 
persons. 

A  device  sometimes  used  is  the  "set  back."  If  we  are 
comparing  two  curves,  one  of  which  is  supposed  to  represent 
the  cause  of  the  other,  we  may  plot  the  causal  curve  on  the 
true  dates  and  we  may  set  back  the  dates  of  the  resulting 
curve  by  an  amount  equal  to  the  lag.  Correlation  will 
then  be  indicated  by  the  correspondence  of  the  curves. 
This  presupposes  that  the  amount  of  the  lag  is  known. 

In  comparing  lagging  curves  which  are  apparently  correl- 
ative it  is  important  to  distinguish  between  cause  and 
effect.  As  we  have  reiterated,  it  is  not  the  function  of 
correlation  to  demonstrate  causality. 


418  CORRELATION 

Fig.  52  is  an  example  of  the  use  of  the  set  back.  This  is 
a  correlation  between  typhoid  fever  deaths  and  atmospheric 
temperatures,  the  deaths  being  set  back  two  months. 

Coefficient  of  correlation  and  the  lag.  —  It  is  possible  to 
,deal  with  the  lag  analytically  instead  of  graphically.  We 
may  find  that  by  comparing  two  series  of  statistics,  date 
for  date,  the  coefficient  of  correlation  is  low;  by  setting  one 
series  back  a  day  and  recomputing  the  coefficient  we  may 
find  it  higher;  by  setting  back  two  days  the  coefficient  may 
be  higher  still;  and  by  using  greater  set  backs  the  coeffi- 
cient may  increase  to  a  maximum,  and  beyond  that  point 
it  may  decrease.  The  set  back  whicrTproduces  the  highest 
correlation  may  be  taken  as  a  measure  of  the  lag. 

All  such  matters  as  these  are  fully  discussed  in  the  text- 
books of  general  statistics. 

Other  secondary  correlations.  —  Sometimes  the  second- 
ary character  of  a  correlation  is  not  as  clearly  revealed  as 
in  the  case  of  two  plotted  lines  with  common  abscissae.  It 
has  been  noticed  that  poliomyelitis  cases  seem  to  follow 
the  river  valleys;  what  is  the  real  correlation  here?  It 
does  not  appear  to  be  a  direct  correlation.  One  says  that 
fleas  are  correlated  with  the  river  valleys,  and  that,  secon- 
darily, the  disease  is  correlated  with  the  fleas;  another  says 
that  the  lines  of  transportation  are  along  the  river  valleys 
and  that  the  real  correlation  is  between  poliomyelitis  and 
the  contact  of  people  incident  to  intercommunication. 

The  whole  matter  of  correlation  is  almost  inseparable 
from  the  science  of  logic. 

The  epidemiologist's  use  of  correlation.  —  Epidemiology, 
a  branch  of  medical  science,  is  based  fundamentally  on  the 
laws  of  cause  and  effect.  The  epidemiologist  is  continually 
searching  for  the  cause  of  outbreaks  of  disease  in  order  that 
they  may  be  checked  and  future  outbreaks  prevented.  In 
his  studies  he  uses  statistics  continually  and  is  of  necessity 


THE  EPIDEMIOLOGIST'S  USE  OF  CORRELATION     419 

mightily  interested  in  correlation.  The  successful  epi- 
demiologist must  have  a  nose  for  facts,  must  be  able  to 
analyze  these  facts  skillfully  and  draw  logical  conclusions 
from  them. 

The  influence  of  a  particular  factor  as  a  cause  of  disease 
is  often  studied  by  means  of  statistics.  For  example,  the 
filtration  of  a  public  water-supply  may  be  followed  by  a 
reduction  of  the  typhoid  fever  death-rate  among  the  water 
takers.  This  is  a  sort  of  correlation,  —  one  change  being 
followed  by  another.  We  know,  moreover,  by  inductive 
reasoning  from  many  such  occurrences  in  the  past  and  also 
from  experimental  evidence  that  this  is  a  correlation  which 
implies  causality.  In  using  this  method  of  reasoning,  how- 
ever, it  is  important  to  know  that  the  change  in  the  water- 
supply  was  the  only  change  which  occurred. 

There  are  scores  of  instances  where  this  method  of 
reasoning  has  been  used.  In  Panama  the  abolition  of  the 
mosquito  reduced  the  death-rate  from  yellow  fever.  The 
evidence  points  to  this  as  a  clear-cut  case  not  only  of  cor- 
relation, but  causality.  In  Panama  also  the  malaria  has 
been  greatly  reduced  since  the  anti-mosquito  work  was  be- 
gun. But  here  we  find  that  quinine  has  been  used  as  an 
additional  preventative.  In  this  case  therefore  we  have  had 
two  factors  changing  at  about  the  same  time.  From  ex- 
perimental evidence  there  is  no  doubt  in  regard  to  the 
causal  relations  between  malaria  and  the  Anopheles  mos- 
quito, but  statistically  the  evidence  is  not  as  strong  as  in 
the  case  of  yellow  fever. 

In  some  of  the  old  studies  of  typhoid  fever  it  was  found 
that  the  death-rate  decreased  after  the  introduction  of  a 
sewerage  system.  This  was  accompanied  by  an  abolition 
of  house  privies.  Now  it  was  probably  the  abolition  of 
the  old  privies,  not  the  building  of  the  new  sewers  which 
produced  the  result.  In  other  cases  a  public  water-supply 


420  CORRELATION 

was  installed  at  the  same  time  that  the  sewers  were  built. 
A  reduction  in  the  typhoid  death-rate  following  these  events 
may  have  been  due  to  either  or  to  both. 

The  fact  should  not  be  overlooked  that  when  epidemics 
occur  there  is  not  infrequently  more  than  a  single  factor 
involved.  Sometimes  an  outbreak  can  be  traced  to  a 
single  initial  case,  but  just  as  in  lighting  a  fire  the  match  is 
applied  to  the  paper,  the  burning  paper  sets  fire  to  the 
kindling  and  the  burning  kindling  sets  fire  to  the  coal,  so  a 
single  case  may  start  infections  which  may  be  scattered  in 
various  ways.  It  is  important  for  the  epidemiologist  to 
find  all  of  these  methods  of  transmission. 

Sometimes  the  epidemiologist  is  obliged  to  base  his  action 
upon  statistics  which  show  correlation  without  waiting  to  de- 
termine whether  this  correlation  also  means  causation.  For 
example,  in  the  recent  pandemic  of  influenza  a  certain  vac- 
cine, supposed  to  have  a  prophylactic  value,  was  used  upon 
several  hundred  persons.  The  question  arose,  "  Shall  this 
vaccine  be  distributed  and  generally  used?  "  The  data  first 
collected  showed  a  fair  degree  of  correlation  between  the  use 
of  the  vaccine  and  apparent  protection  against  the  disease, 
and  on  the  strength  of  this  finding  the  vaccine  was  dis- 
tributed. Later  studies,  however,  failed  to  corroborate  the 
correlation  at  first  noticed,  and  showed  that  there  was  no 
causal  relation  between  the  use  of  the  vaccine  and  failure  of 
persons  to  take  the  disease.  It  was  really  a  case  of  correla- 
tion without  causation,  —  post  hoc  non  propter  hoc.  And  yet 
the  health  authorities,  compelled  to  take  action  one  way  or 
the  other,  were  right  in  basing  action  on  the  supposed  corre- 
lation. 


EXERCISES  AND  QUESTIONS  421 

EXERCISES  AND    QUESTIONS 

1.  Is  there  a  correlation  between  epidemics  of  poliomyelitis  and  rain- 
fall?    [See  Am.  J.  P.  H.,  Sept.,  1917,  p.  813.] 

2.  Is  there  a  higher  correlation  between  flies  and  diarrhoeal  diseases 
among  children  than  between  diarrhcEal  diseases  and  other  factors? 
[See  Am.  J.  P.  H.,  Feb.,  1916,  p.  143,  also  Mar.,  1914,  p.  184.] 

3.  Is  there  a  correlation  between  pneumonia  and  influenza?     Is 
there  a  causal  relation?     [See  Am.  J.  P.  H.,  Apr.,  1916,  p.  316.] 

4.  Is  there  a  correlation  between  tuberculosis  and  housing?     [See 
Am.  A.  J.  P.  H.,  Jan.  1913,  p.  24.] 

5.  Look  up  Dr.  Fulton's  extravaganza  on  the  subject  of  statistical 
logic  as  applied  to  the  problem  of  prostitution.     [See  Am.  J.  P.  H., 
July,  1913,  p.  661.] 

6.  Study  the  correlation  between  plague  and  fleas.     [Am.  J.  P.  H., 
Aug.,  1918,  p.  572.]     Is  there  strong  presumptive  evidence  that  in- 
fantile paralysis  is  spread  by  fleas? 

7.  Express  Mill's  three  canons  of  logic  in  your  own  words. 

8.  Give  examples  of  each  in  the  field  of  epidemiology. 

9.  What  is  meant  by  quantitative  induction?     What  part  do  statis- 
tics play  in  this?     [See  Jevon's  Lessons  in  Logic,  Chap.  XXIX.] 


CHAPTER  XIV 
LIFE  TABLES 

To  the  popular  mind  there  is  something  mysterious  and 
awesome  about  a  life  table.  The  insurance  agent,  wishing 
to  sell  you  a  policy,  asks  your  age,  consults  a  printed  table 
and  tells  your  "expectation  of  life "  as  so  many  years.  What 
does  this  mean  and  how  does  he  arrive  at  this  expectation  of 
life  ?  It  does  not  mean  that  you  will  live  so  many  years  and 
then  die.  It  means  that  it  has  been  found  in  the  past  that 
most  men  who  have  attained  your  age  have  lived  so  many 
years  after  reaching  that  age.  It  cannot  apply  to  everyone. 
You  may  live  to  be  a  hundred  years  old  or  you  may  die 
to-morrow.  The  future  is  uncertain  for  every  individual. 
But  the  probability  of  your  future  longevity  can  be  deter- 
mined by  making  a  statistical  study  of  a  large  group  of  people 
who  have  attained  your  age,  to  find  out  the  average  number 
of  years  which  they  lived  after  reaching  that  age.  Instead 
of  using  the  average,  i.e.,  the  mean  we  might  find  the  median 
number  of  years  lived,  or  even  the  mode.  All  three  methods 
have  been  suggested,  but  that  based  on  the  mean  is  the  one 
commonly  used.  Thus  we  see  that  there  is  nothing  mysteri- 
ous about  the  "  expect  at  ion  of  life";  it  has  no  divine  origin. 
It  is  merely  the  application  of  the  ordinary  methods  of 
statistics  to  the  experience  of  mankind  in  living  beyond  a 
given  age. 

Probability  of  living  a  year.  —  Although  the  expectation 
of  life  is  used  by  insurance  agents  to  impress  the  prospective 
purchaser  with  the  fleeting  character  of  human  life,  the  rates 

422 


PROBABILITY  OF  LIVING  A  YEAR  423 

of  insurance  are  not  based  directly  on  this  expectation,  but 
on  the  probability  of  a  person  of  given  age  living  to  be  one 
year  older.  It  is  this  chance  of  living  from  year  to  year, 
coupled  with  the  growth  of  money  at  compound  interest 
which  determines  what  premium  the  insured  at  any  age  must 
pay.  These  actuarial  methods  are  too  complicated  to  be 
entered  into  here.  In  the  very  early  days  life  insurance  was 
virtually  a  lottery;  now  it  is  based  on  experience.  If,  as  a 
result  of  better  living  conditions,  the  longevity  of  the  insured 
is  greater  than  the  experience  upon  which  the  rates  were 
based,  the  insurance  company  is  the  gainer  because  the 
premiums  are  continued  for  a  longer  time  and  the  final  pay- 
ment of  the  policy  is  postponed.  If  the  company  is  p,  so- 
called  mutual  company,  the  benefit  of  increased  longevity 
of  the  insured  is  distributed  among  the  policy  holders  in  the 
form  of  rebates.  But  should  the  longevity  of  the  insured 
prove  to  be  less  than  the  experience  upon  which  the  rates 
were  based  the  opposite  condition  would  prevail. 

What  is  the  chance  of  a  person  living  from  year  to  year? 
Obviously  it  is  one  minus  the  chance  of  dying.  The  chance 
of  dying  within  one  year  at  any  age  is  nothing  else  than  our 
old  friend  the  specific  death-rate  for  the  given  age.  Thus  if 
at  age  20  the  specific  death-rate  is  7.80  per  1000,  the  chance 
of  dying  within  the  year  is  780  in  100,000,  0.0078  in  1,  or  1 
chance  in  128;  at  age  50  the  chance  is  0.01378,  or  1  in  73; 
at  age  70  it  is  0.06199  or  1  in  16;  at  age  80  it  is  0.14447,  or 
1  in  7;  at  age  90,  it  is  0.45454,  or  1  in  2.2. 

The  chance  of  living  through. the  year  is  1  less  the  chance 
of  dying.  At  age  20  the  chance  of  living  through  the 
year  is  99,220  in  100,000,  i.e.,  0.9920;  at  age  50  it  is  0.98622; 
at  age  70,  0.93801 ;  at  age  80  it  is  0.85553;  at  90  it  is  0.54546. 
Or,  to  put  it  in  another  form,  —  at  age  20  the  chance  of  living 
a  year  is  99.2  in  a  hundred;  at  age  50,  98.6;  at  age  70,  93.8; 
at  age  80,  85.5;  at  age  90,  54.5  in  a  hundred. 


424 


LIFE  TABLES 


Thus  a  column  showing  for  each  age  of  life  the  probability 
of  living  a  year  can  be  made  by  subtracting  the  yearly 
specific  death-rates  from  unity,  and  expressing  the  results 
in  decimal  parts  of  1.  We  might  call  these  specific  life-rates, 
as  they  are  the  converse  of  the  specific  death-rates. 

This  specific  life-rate  is  never  used  in  ordinary  discussion, 
and  there  is  little  reason  for  using  it,  as  it  is  probably  better 
to  think  in  terms  of  specific  death-rates.  It  is  the  deaths 
which  we  are  always  trying  to  postpone.  A  table  of  specific 
death-rates  and  specific  life-rates  would  look  like  this. 


TABLE   143 

SPECIFIC  DEATH-RATES  AND   SPECIFIC  LIFE-RATES 
(Abridged  from  the  American  Experience  Mortality  Table.) 


Age.  " 

Population  alive  at 
mid-year. 

Specific  death-rate  per 
100,000  (number  dying 
annually). 

Specific  life-rate  per  100,000 
(number  living  through 
the  year). 

(1) 

(2) 

(3) 

(4) 

10 

100,000 

749 

99,251 

20 

100,000 

780 

99,220 

30 

100,000 

843 

99,157 

40 

100,000 

979 

.  99,021 

50 

100,000 

1,378 

98,622 

60 

100,000 

2,669 

97,331 

70 

100,000 

6,199 

93,801 

80 

100,000 

14,447 

85,553 

90 

100,000 

45,454 

54,546 

One  reason  why  specific  death-rates  are  not  used  more 
commonly  is  because  people  do  not  clearly  understand  them. 
The  base,  i.e.,  100,000  persons,  remains  constant  for  all  ages. 
Actually  the  number*  of  persons  alive  is  constantly  decreasing 
as  age  advances.  One  says  "you  start  with  100,000  persons 
at  age  10  and  kill  off  749  in  one  year,  but  the  next  year  you 
have  100,000  again.  I  don't  understand  it." 


MORTALITY  TABLES 


425 


Now  life  tables  are  definitely  related  to  specific  death-rates 
and  they  take  into  account  this  decreasing  population. 

Mortality  tables.  —  In  order  to  make  a  life  table  we  may 
first  select  some  large  class  of  people  and  determine  the 
specific  death-rates  for  each  year  of  age.  We  start  with  a 
certain  number  of  people  alive  at  a  certain  age.  The  in- 
surance companies  commonly  use  age  10  because  most 
insured  persons  are  older  than  that,  but  we  might  use  any 
other  age.  We  might  use  age  0,  and  in  making  a  life  table 

i  for  a  general  population  this  would  be  done.  As  an  illustra- 
tion, however,  let  us  take  the  American  Experience  Mortality 
Table,  which  starts  at  age  10  and  which  is  limited  to  males. 
Another  reason  for  taking  age  10  is  that  it  is  a  round  number 

i  not  far  from  the  age  at  which  the  specific  death-rate  is  the 
lowest. 

For  convenience  we  start  with  100,000  as  a  round  number 
of  persons  alive  at  age  10.  This  number  is  called  the  radix 
of  the  computation.  We  might  use  a  million  or  a  thousand, 
but  the  former  is  hardly  warranted  by  the  precision  of  our 
specific  death-rates,  while  the  latter  gives  too  many  decimals. 
In  the  table,  column  (1)  gives  the  age,  and  column  (5)  the 
corresponding  specific  death-rates  obtained  from  the  original 
data.  In  column  (2)  we  start  with  100,000  persons  alive  at 
age  10,  of  these 

lived  to  age 


92,637 

85,441 

78,106 

69,804 

57,917 

38,569 

14,474 

847 

0 


20 
30 
40 
50 
60 
70 
80 
90 
96 


These  figures  were  obtained  as  follows:  — 100,000  were 
alive  at  the  beginning  of  age  10  and  749  -per  100,000  died 


426 


LIFE  TABLES 


TABLE   144 
AMERICAN  EXPERIENCE  MORTALITY  TABLE 


Age. 

Num- 
ber 
living. 

Num- 
ber 
dying. 

No.  of 
years 
expect- 
ation of 
life. 

No.  dy- 
ing of 
each 
100,000 
annually. 

Age. 

Num- 
ber 
living. 

Num- 
ber 
dying. 

No.  of 
years 
expect- 
ation of 
life. 

No.  dy- 
ing of 
each 
100,000 
annually. 

(1) 

(2) 

(3) 

(4) 

(5) 

(1) 

(2) 

•     (3) 

(4) 

(5) 

10 

100,000 

749 

48.72 

749 

53 

66,797 

1,091 

18.79 

1,633 

11 

99,251 

746 

48.08 

752 

54 

65,706 

1,143 

18.09 

1,740 

12 

98,505 

743 

47.45 

754 

55 

64,563 

1,199 

17.40 

1,857 

13 

97,762 

740 

46.80 

757 

56 

63,364 

1,260 

16.72 

1,988 

14 

97,022 

737 

46.16 

760 

57 

62,104 

1,325 

16.05 

2,133 

15 

96,285 

735 

45.50 

763 

58 

60,779 

1,394 

15.39 

2,294 

16 

95,550 

732 

44.85 

766 

59 

59,385 

1,468 

14.74 

2,472 

17 

94,818 

729 

44.19 

769 

60 

57,917 

1,546 

14.10 

2,669 

18 

94,089 

727 

43.53 

773 

61 

56,371 

1,628 

13.47 

2,888 

19 

93,362 

725 

42.87 

776 

62 

54,743 

1,713 

12.86 

3,129 

20 

92,637 

723 

42.20 

780 

63 

53,030 

1,800 

12.26 

3,394 

21 

91,914 

722 

41.53 

785 

64 

51,230 

1,889 

11.67 

3,687 

22 

91,192 

721 

40.85 

791 

I):, 

49,341 

1,980 

11.10 

4,013 

23 

90,471 

720 

40.17 

796 

36 

47,361 

2,070 

10.54 

4,371 

24 

89,751 

719 

39.49 

801 

67 

45,291 

2,158 

10.00 

4,765 

25 

89,032 

718 

38.81 

806 

68 

43,133 

2,243 

9.47 

5,200 

26 

88,314 

718 

38.12 

813 

69 

40,890 

2,321 

8.97 

5,676 

27 

87,596 

718 

37.43 

820 

70 

38,569 

2,391 

8.48 

6,199 

28 

86,878 

718 

36.73 

826 

71 

36,178 

2,448. 

8.00 

6,766 

29 

86,160 

719 

36.03 

834 

72 

33,730 

2,487 

7.55 

7,373 

30 

85,441 

720 

35.33 

843 

73 

31,243 

2,505 

7.11 

8,018 

31 

84,721 

721 

34.63 

851 

74 

28,738 

2,501 

6.68 

8,703 

32 

84,000 

723 

33.92 

861 

75 

26,237 

2,476 

6.27 

9,437 

33 

83,277 

726 

33.21 

872 

76 

23,761 

2,431 

5.88 

10,231 

34 

82,551 

729 

32.50 

883 

77 

21,330 

2,369 

5.49 

11,106 

35 

81,822 

732 

31.78 

895 

78 

18,961 

2,291 

5.11 

12,083 

36 

81,090 

737 

31.07 

909 

79 

16.670 

2,196 

4.74 

13,173 

37 

80,353 

742 

30.35 

923 

80 

14,474 

2,091 

4.39 

14,447 

38 

79,611 

749 

29.62 

941 

81 

12,383 

1,964 

4.05 

15,860 

39 

78,862 

756 

28.90 

959 

82 

10,419 

1,816 

3.71 

17,430 

40 

78,106 

765 

28.18 

979 

83 

8,603 

1,648 

3.39 

19,156 

41 

77,341 

774 

27.45 

1,001 

84 

6,955 

1,470 

3.08 

21,136 

42 

76,567 

785 

26.72 

1,025 

85 

5,485 

1,292 

2.77 

23,555 

43 

75,782 

797 

26.00 

1,052 

86 

4,193 

1,114 

2.47 

26,568 

44 

74,985 

812 

25.27 

1,083 

87 

3,079 

933 

2.18 

30,302 

45 

74,173 

828. 

24.54 

1,116 

88 

2,146 

744 

1.91 

34,669 

46 

73,345 

848 

23.81 

1,156 

89 

1,402 

555 

1.66 

39,586 

47 

72,497 

870 

23.08 

1,200 

90 

847 

.385 

1.42 

45,454 

48 

71,627 

896 

22.36 

1,251 

91 

462 

246 

1.19 

53,247 

49 

70,731 

927 

21.63 

1,311 

92 

216 

137 

0.98 

63,426 

50 

69,804 

962 

20.91 

1,378 

93 

79 

58 

0.80 

73,418 

51 

68,842 

1,001 

20.20 

1,454 

94 

21 

18 

0.64 

85,714 

THE  "VIE  PROBABLE"  427 

• 

during  the  year.  Consequently,  the  number  alive  at  age  11 
was  100,000  —  749  =  99,251.  In  the  next  year  the  specific 
death-rate  was  752  per  100,000.  The  number  dying  was, 

752 
therefore,  99,251  X  inrtnnn  =  746,  and  the  number  alive  at 

XUUjUUU 

age  12  was  99,251  -  746  =  98,505.  And  so  on.  The  num- 
ber dying  each  year  is  given  in  column  (3),  the  number  living 
in  column  (2).  At  age  96  all  were  dead. 

These  are  the  facts  of  the  case,  now  how  shall  we  use  them  ? 
There  are  three  ways,  which  correspond  to  the  mode,  the 
median  and  the  mean,  and  they  are  called  respectively  the 
"most  probable  life-time,"  the  "Vie  Probable,"  and  the 
"Expectation  of  Life." 

F  The  <5  most  probable  life-time."  —  The  figures  in  column  3 
form  a  frequency  curve,  the  mode  of  which  is  2505.  There 
are  more  deaths  at  age  73  (i.e.,  age  73-74)  than  at  any  other 
| '  age.  73  is  the  fashionable,  modish  age  to  die.  The  chance 
of  dying  at  that  age  is  greater  than  at  any  other  age. 

The  difference  between  a  given  age  and  73  years  is  called 
"the  most  probable  life-time."  At  age  10,  it  is  73  -  10  = 
63;  at  age  20  it  is  53;  and  so  on.  Above  the  age  73  the 
"most  probable  life-time"  becomes  a  negative  quantity,  and 
this  is  the  objection  to  the  use  of  this  computation.  It  is 
applicable  only  to  the  first  part  of  the  frequency  curve. 

The  "Vie  Probable."  —  The  "Vie  Probable"  is  the 
number  of  years  which  a  person  (at  a  stated  age)  has  an  even 
chance  of  living.  It  is  the  difference  between  a  given  age 
and  the  age  at  which  the  number  of  persons  alive  is  one-half 
the  number  alive  at  the  given  age.  The  latter  is  the  median 
age  to  which  the  persons  who  passed  the  given  age  lived. 

At  age  10  there  are  100,000  persons  alive.  One-half  of 
this  number,  i.e.,  50,000,  are  alive  at  age  64.5  ±.  Hence 
64.5  —  10  =  54.5  is  the  "vie  probable."  In  this  period  of 
time  the  chance  of  living  or  dying  is  just  even. 


428  LIFE  TABLES 

At  age  20,  there  are  92,637  persons  alive.  One-half  of  this 
number,  i.e.,  46,318,  were  still  alive  at  age  66.5.  Hence  the 
"vie  probable,"  for  age  20  is  66.5  -  20  =  46.5  years. 

The  "  Expectation  of  Life."  — The  ''Expectation  of 
life"  means  the  average  number  of  years  that  persons  of  a 
given  age  will  probably  survive.  It  is  obtained  by  finding 
the  average  of  the  lengths  of  life  of  all  the  persons  who  lived 
beyond  the  given  age. 

Thus  of  the  100,000  alive  at  age  10,  3  lived  to  the  age  of  95, 
that  is,  they  lived  for  (95  —  10  = )  85  years  after  the  age  of 
10.  21  lived  to  age  94,  i.e.,  84  years.  But  these  21  include 
the  3  who  lived  to  age  95,  so  there  were  18  who  lived  84 
years.  79  lived  83  years,  but  these  include  both  the  3  and 
the  18,  so  in  addition  to  them  (79  —  21  = )  58  lived  82  years. 
And  so  on.  The  weighted  averages  of  all  of  these  lives  gives 
what  is  called  the  expectation  of  life.  These  results  are 
given  in  column  (4). 

In  obtaining  the  figures  for  column  (4)  it  is  most  con- 
venient to  begin  at  the  higher  ages  and  work  backward. 

At  the  beginning  of  age  95,  there  were  3  persons  alive;  at 
the  end  there  were  none  alive.  Not  knowing  at  what  part 
of  the  year  they  died  the  best  assumption  is  that  they  died 
(on  an  average)  at  the  middle  of  the  year,  i.e.,  they  lived 
one-half  year.  Hence  at  age  95,  the  average  length  of  the 

O     vx      1 

lives  was  — ^— -  =  0.50  year.    This  is  the  expectation  of  life 

at  age  95. 

At  age  94,  21  persons  were  alive.  3  of  these  lived  1J  years 
each;  the  other  18  died  within  the  year,  and  may  be  said  to 
have  lived  one-half  year.  Hence  we  have : 

3  X  1.5  =  4.5 
18  X  0.5  =  9.0 
21  13.5  and  13.5  ~-  21  =  0.64  yr. 

Hence  at  age  94  the  expectation  of  life  is  0.64  year. 


COMPARISON  OF  THE  THREE  RESULTS 


429 


At  age  93  we  have: 

3  X  2.5  =  7.5 
18  X  1.5  =  27.0 
58  X  0.5  =  29.0 
79  63.5,  and  63.5  X  79  =  0.80  year. 

In  this  way  we  find  that  at  age  10,  the  average  number  of 

years  lived  by  those  who  passed  ^age  10,  was  48.72  years. 

At  age  20  it  was  42.20  years;  at  age  30  it  was  35.33  years,  etc. 

Comparison  of  the  three  results.  —  The  U.  S.  Life  Tables 

*  for  1910  give  the  " complete  expectation  of  life"  (computed 

i  on  the  basis  of  the  mean),  and  from  the  tables  may  be  ob- 

I  tained  the  "most  probable  life-time"  (based  on  the  mode) 

;  and  the  "vie  probable"  (based  on  the  median).     The  follow- 

!  ing  figures  give  the  results  for  age  zero,  that  is,  they  show 

the  expectation  of  life  at  birth. 


TABLE   145 

COMPARISON  OF  "EXPECTATION  OF  LIFE,"  "VIE  PROB- 
ABLE" AND   "MOST  PROBABLE  LIFE-TIME" 


Original  registration  states. 

Expecta- 
tion of  life. 
(Mean.) 

"  Vie  prob- 
able." i 
(Median.) 

Most    prob- 
able i  life- 
time. 
(Mode.) 

(1) 

(2) 

(3) 

(4) 

White  males  ,  

50.23 

59.30 

74.0 

White  females   ... 

53.62 

63.27 

73.5 

Negro  males  

34.05 

34.85 

59.5 

Negro  females  

37.67 

40.58 

65.5 

White  males  in  cities 

47  32 

55  00 

68  5 

White  males  in  rural  part   

55.06 

65.33 

76.5 

White  females  in  cities  

51.39 

60.73 

71.5 

White  females  in  rural  part  

57.35 

67.38 

76.5 

Males  in  Massachusetts 

49.33 

58.82 

69.5 

Females  in  Massachusetts  

53.06 

62.74 

74.5 

1  Approximate. 


430  LIFE  TABLES 

Life  tables  based  on  living  population.  —  Life  tables  are 
usually  computed  in  another  way.  They  are  based  on  the 
population  living  at  each  age  as  shown  by  the  census  returns 
or  by  data  collected  by  the  insurance  companies.  Thus  we 
may  assume  that  the  figures  in  column  (2)  have  been  ob- 
tained in  this  way.  If  we  start  with  100,000  persons  alive 
at  age  10  and  find  that  99,251  were  alive  at  age  11  then  the 
number  of  deaths  during  the  year  must  have  been  100,000  - 
99,251,  or  749.  Between  ages  11  and  12  the  deaths  were 
99,251  -  98,505,  or  746;  and  so  on.  By  this  method  we 
compute  the  deaths,  and  we  may  also  compute  the  specific 
death-rates  for  each  age.  This  method  justifies  the  use  of 
the  term  life  tables,  as  the  results  are  based  on  the  living  and 
not  on  the  dying.  It  is  obvious  that  migrations  of  population 
interfere  somewhat  with  this  method.  It  is  obvious,  also, 
that  concentrations  of  population  on  the  round  numbers 
present  another  difficulty.  As  a  matter  of  practice  the 
ragged  data  must  be  smoothed  out  before  a  life  table  can  be 
constructed;  otherwise  the  computed  expectations  of  life 
would  themselves  be  erratic.  These  errors  of  round  numbers 
creep  into  the  computations  of  specific  death-rates,  so  that 
in  any  case  it  is  necessary  to  do  a  certain  amount  of  "  smooth- 
ing" before  computing  life  tables.  One  method  commonly 
used  is  that  known  as  "osculatory  interpolation,"  which 
may  be  found  described  in  such  books  as  Vital  Statistics  Ex- 
plained, by  Burn. 

Still  another  method  of  computing  a  life  table  is  to  base  it 
wholly  on  the  distribution  of  deaths,  making  use  of  certain 
mathematical  formulas  for  frequency  curves.1 

Mathematical  formula  for  computing  the  expectation  of 
life.  —  There  is  a  mathematical  formula  for  the  computa- 
tion of  the  expectation  of  life  by  the  use  of  which  the  labor 
may  be  shortened.  It  is  usually  stated  as  follows: 

1  Arne  Fisher.  Note  on  the  Construction  of  Mortality  Tables  by 
means  of  Compound  Frequency  Curves.  Proc.  Casualty  Actuarial  and 
Statistical  Society  of  America,  Vol.  IV,  Pt.  1,  No.  9. 


EARLY  HISTORY  OF  LIFE  TABLES  431 


o 

e,  =  expectation  of  life,  in  years,  at  age  x. 

lx  =  number  of  persons  living  at  age  x. 
l(x+i>  =  number  of  persons  living  at  age  x  +  1. 
/(r+2)  =  number  of  persons  living  at  age  x  +  2,  etc. 

For  a  more  detailed  description  of  these  methods  the 
reader  is  referred  to  such  books  as  United  States  Life  Tables, 
1910,  Bureau  of  the  Census,  prepared  by  Prof.  James  W. 
Glover  and  published  in  1916;  Life  Assurance  Primer,  by 
Henry  Moir;  Vital  Statistics,  by  Newsholme;  Mortality 
Laws  and  Statistics,  by  Robert  Henderson. 

Early  history  of  life  tables.  —  It  is  not  surprising  that 
most  of  the  life  tables  which  have  been  computed  have  been 
confined  to  males  of  insurable  age.  Halley,  the  British 
astronomer,  famous  for  the  comet  which  bears  his  name,  was 
the  first  to  use  the  method.  This  was  in  1692  and  related 
to  the  town  of  Breslau.  Other  famous  tables  are  the  North- 
ampton Table  of  1762,  the  Carlisle  Table  of  1815  and  Dr. 
Farr's  English  Table  of  1851. 

In  1843  seventeen  American  insurance  companies  com- 
bined their  experiences  and  published  a  table  known  as  the 
Actuaries  or  Combined  Experience  Table.  It  was  based  on 
84,000  policies.  The  American  Experience  Table  of  Mor- 
tality, now  recognized  by  the  insurance  companies  as  the 
standard  for  America,  was  formed  by  Sheppard  Homans  in 
1868.  It  is  supposed  to  have  been  based  on  the  experience  of 
1  the  Mutual  Life  Insurance  Company  of  New  York. 

In  1869  the  HM  Table  was  published  in  England.  HM 
means  Healthy  Males.  It  was  based  on  180,000  policies. 
Then  there  is  an  0M  Table  (ordinary  life,  males)  based  on 
over  400,000  lives.  This  is  the  Canadian  standard. 


432 


LIFE  TABLES 


Recent  life  tables.  —  In  1898  Dr.  Samuel  W.  Abbott 
published  in  the  annual  report  of  the  Massachusetts  State 
Board  of  Health  for  that  year,1  a  life  table  for  Massachusetts. 
This  is  one  of  our  best  American  papers  on  the  subject. 

Dr.  Guilfoy,  the  statistician  of  the  New  York  City  Board 
of  Health,  has  published  the  following  interesting  comparison 
between  the  expectations  of  life  in  1879-81  and  1909-11. 
The  changes  which  have  taken  place  during  the  interval  are 
striking.  The  figures  are  as  follows: 

TABLE   146 

APPROXIMATE  LIFE  TABLES  FOR  THE   CITY  OF  NEW 

YORK  BASED   ON   MORTALITY  RETURNS  FOR  THE 

TRIENNIA   1879-1881  AND   1909-1911 


Years  of 
mor- 

Expectation of  life, 
1879  to  1881. 

Expectation  of  life, 
1909  to  1911. 

Gain(+)orloss(-)in 
years  of  expectancy. 

tality, 
««es. 

Males. 

Fe- 
males. 

Per- 
sons. 

Males. 

Fe- 
males. 

Per- 
sons. 

Males. 

Fe- 
males. 

Per- 
sons. 

(1) 

(2) 

'    (3) 

(4) 

(5) 

(6) 

(7) 

(8) 

(9) 

(10)     - 

-5 

39.7 

42.8 

41.3 

50.1 

53.8 

51.9 

+  10.4 

+  11.0 

+  10.6 

5 

44.9 

47.7 

46.3 

49.4 

52.9 

51.1 

+  4.5 

+  5.2 

+  4.8 

10 

42.4 

45.3 

43.8 

45.2 

48.7 

46.9 

+  2.8 

+  3.4 

+  3.1 

15 

38.2 

41.2 

39.7 

40.8 

44.2 

42.5 

+  2.6 

+  3.0 

+  2.8 

20 

34.4 

37.3 

35.8 

36.6 

40.0 

38.3 

+  2.2 

+  2.7 

+  2.5 

25 

31.2 

34.0 

32.6 

32.7 

36:0 

34.3 

+  1.5 

+  2.0 

+  1.7 

30 

28.2 

31.0 

29.6 

28.9 

32.1 

30.5 

+  0.7 

+  1.1 

+  0.9 

35 

25.3. 

28.1 

26.7 

25.4 

28.4 

26.9 

+  0.1 

+  0.3 

+  0.2 

40 

22.5 

25.2 

23.9 

22.1 

24.7 

23.4 

-  0.4 

+  0.5 

-  0.5 

45 

19.8 

22.4 

21.1 

18.9 

21.1 

20.0 

-  0.9 

-     .1 

-  1.1 

50 

17.2 

19.4 

18.3 

15.9 

17.7 

16,8 

-  1.3 

7 

-  1.5 

55 

14.5 

16.4 

15.4 

13.2 

14.6 

13.9 

-  1.3 

-     .'8 

-  1.5 

60 

12.2 

13.8 

13.0 

10.8 

11.8 

11.3 

-  1.4 

-     .0 

-  1.7 

65 

9.9 

11.2 

10.5 

8.8 

9.4 

9.1 

-  1.1 

-     .8 

-  1.4 

70 

8.5 

9.3 

8.9 

6.9 

7.5 

7.2 

-  1.6 

-     .8 

-  1.7 

75 

7.1 

7.5 

7.3 

5.3 

5.7 

5.5 

-  1.8 

g 

-  1.8 

80 

6.2 

6.5 

6.4 

4.1 

4.5 

4.3 

-  2.1 

-  2^0 

-  2.1 

85+ 

5.4 

5.5 

5.5 

2.0 

2.4 

2.2 

-  3.4 

-  3.1 

-  3.3 

+24.8 

+28.7 

+26.6 

Balance  

-15.3 

-17.6 

-16.6 

+  9.5 

+11.1 

+  10.0 

See  State  Sanitation,  Vol.  II,  p.  300,  by  G.  C.  Whipple. 


A  FEW  COMPARISONS  433 

United  States  life  tables.  —  In  1916  the  Bureau  of  the 
Census  published  a  special  report  entitled  United  States 
Life  Tables,  1910,  prepared  under  the  direction  of  Prof. 
James  W.  Glover  of  the  University  of  Michigan.  This  was 
the  first  report  of  its  kind  in  America.  The  tables  are  based 
on  the  general  unselected  population,  and,  therefore,  differ 
from  the  life  tables  of  the  insurance  companies.  The  radix 
is  100,000  at  age  0.  The  data  were  obtained  from  the  U.  S. 
Census  of  1910.  Expectations  of  life  are  computed  by 
months  up  to  one  year  of  age,  and  after  that  by  years  up  to 
age  106.  Separate  tables  are  given  for  males,  for  females 
and  for  both  sexes  combined;  there  are  separate  tables  also 
for  negroes  and  whites,  and  for  native  and  foreign  born 
whites;  for  cities  and  for  rural  districts,  —  all  of  these  re- 
lating to  the  population  of  the  original  registration  states, 
namely,  the  New  England  states,  New  York,  New  Jersey, 
Indiana,  Michigan  and  the  District  of  Columbia.  Separate 
tables  for  males  and  for  females  are  given  for  the  states  of 
Indiana,  Massachusetts,  Michigan,  New  Jersey  and  New 
York. 

These  tables  are  well  prepared  and  their  results  are  of  much 
interest.  Besides  giving  the  expectations  of  life  computed 
in  the  usual  way,  computations  are  made  on  the  assumption 
of  a  stationary  population,  that  is  one  where  the  general 
death-rate  is  equal  to  the  general  birth-rate.  .  These  have 
the  advantage  of  excluding  the  effect  of  emigration  results 
and  immigration,  and  from  them  one  can  compare  the  death- 
rates  of  different  communities  for  the  population  above  a 
given  age.  For  these  results  the  reader  is  referred  to  the 
original  report. 

A  few  comparisons.  —  It  will  be  interesting  to  make  a 
few  comparisons  of  the  expectations  of  life  at  certain  ages  for 
different  classes  of  people  and  at  different  ages.  For  greater 
details  the  reader  should  consult  Professor  Glover's  report. 


434 


LIFE  TABLES 


TABLE  147 
EXPECTATIONS   OF  LIFE,   1910 


Age. 
Original  registration  states. 

0 

10 

20 

30 

40 

50 

70 

(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

(7) 

(8) 

Native  white  males  
Native  white  females  

50.58 
54.19 

34^05 
37.67 

47.32 
55.06 
51.39 
57.35 

54.70 
53.86 
49.33 
49.08 
47.89 

51.93 
54.43 
50.30 
52.24 
40.65 
42.84 

49.13 
54.53 
52.22 
55.54 

53.91 
54.09 
51.14 
50.31 
49.40 

43.32 
45.76 
41.75 
43.50 
33.46 
36.14 

40.51 
45.92 
43.51 
46.86 

45.44 
45.57 
42.48 
41.66 
40.79 

35.61 
37.98 
33.71 
35.31 
27.33 
29.61 

32.61 
38.10 
35.52 
39.05 

37.76 
37.76 
34.55 
33.86 
33.01 

28.33 
30.33 
26.03 
27.55 
21.57 
23.34 

25.32 
30.20 
27.88 
31.15 

29.99 
29.81 
26.97 
26.57 

25.88 

21.20 
22.78 
19.08 
20.09 
16.21 
17.65 

18.59 
22.43 
20.53 
23.27 

22.38 
22.10 
19.79 
19.67 
19.28 

9.09 
9.80 
8.40 
8.67 
8.00 
9.22 

8.14 
9.36 
8.99 
9.76 

9.29 
9.17 

8.58 
8.65 
8.58 

Foreign-born  white  males..  . 
Foreign-born  white  females  . 
Negro  males  
Negro  females 

White  males,  in  cities 

White  males  in  rural  part.  .  . 
White  females  in  cities  
White  females  in  rural  part. 

Males  in  Indiana  

Males  in  Michigan 

Males  in  Massachusetts.  .  .  . 
Males  in  New  Jersey  
Males  in  New  York  

The  greater  longevity  of  females  as  compared  with  males 
is  evident  throughout  the  tables.  It  is  greater  for  native 
whites  than  for  foreign  born  whites,  greater  for  whites  than 
for  negroes,  greater  for  rural  districts  than  for  cities.  The 
differences  between  the  states  depend  upon  differences  in  the 
composition  of  the  population,  and  upon  urban  and  rural 
conditions. 

It  is  interesting  also  to  compare  the  specific  death-rates  for 
the  corresponding  ages.  The  relations  between  these  and 
the  expectations  of  life  are  in  a  general  way  reciprocal.  The 
specific  death-rates  are  lower  in  the  rural  districts  than  in 
the  cities,  especially  in  the  early  and  the  later  years;  in  middle 
life  there  is  less  difference.  The  differences  between  whites 
and  negroes  are  very  striking. 


EXERCISES  AND  QUESTIONS 

TABLE   148 
SPECIFIC  DEATH-RATES 


435 


Age. 
Registration  area. 

0 

10 

20 

30 

40 

50 

70 

(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

(7) 

(8) 

Native  white  males  

126.02 

?,  37 

4.82 

7.14 

10.02 

21.20 

57.20 

Native  white  females  

104.60 

?,  06 

4.40 

6.13 

7.76 

11.68 

50.24 

Foreign-born  white  males..  . 
Foreign-born  white  females. 
Negro  males 

2J9  35 

2.47 
2.09 
5  02 

5.10 
3.65 
11  96 

5.80 
5.84 
14  96 

10.53 
8.55 
21  03 

17.92 
14.42 
31  42 

70.79 
67.87 
83  98 

Negro  females  ...       

185  07 

5  18 

10  74 

12  02 

17  50 

25  52 

71  27 

White  males  in  cities  
White  males  in  rural  part.  .  . 
White  females  in  cities  
White  females  in  rural  part  . 

133.80 
103.26 
111.23 
84.97 

2.59 
2.07 
2.23 
1.80 

4.93 
4.83 
4.10 
4.41 

7.22 
5.39 
6.33 
5.46 

12.10 
7.06 
8.83 
6.65 

19.17 
10.65 
14.44 
9.91 

74.20 
52.93 
63.50 
49.92 

EXERCISES  AND    QUESTIONS 

1.  Compare  the  life  table  for  New  Haven  with  that  for  the  U.  S. 
Registration  Area.     [See  Am.  J.  P.  H.,  Aug.,  1918,  p.  580.] 

2.  Compute  a  life  table  for  some  city,  to  be  assigned  by  the  in- 
structor. 

3.  Find  your  own  "probability  of  living  a  year,"  "vie  probable," 
"most  probable  life-time,"  and  "expectation  of  life." 


CHAPTER  XV 
A   COMMENCEMENT   CHAPTER 

This  last  chapter  is  to  be  something  like  the  day  after  col- 
lege commencement.  On  the  day  before  the  student  regards 
his  work  as  finished ;  his  exercises  are  all  completed,  he  has 
passed  his  examinations,  he  is  to  be  graduated.  But  on  the 
day  after  commencement  he  finds  himself  plunging  into  a 
world  of  problems  yet  unsolved;  he  sees  that  most  of  the 
things  he  is  called  upon  to  do  were  not  in  his  curriculum; 
that  he  must  learn  to  do  these  things  for  himself.  Little  by 
little  he  comes  to  realize  that  what  his  stupid  old  profes- 
sors had  been  trying  to  do  was  not  to  tell  him  all  there  was 
to  know  in  the  world  but  to  teach  him  how  to  think 
and  how  to  use  tools.  He  had  heard  much  of  principles, 
and  laws  and  formulae  and  synopses  and  all  that,  and  had 
regarded  them  as  the  dry  parts  of  his  courses  —  the  neces- 
sary evils.  But  little  by  little  he  finds  that  these  general 
principles,  these  almost  self-evident  ideas,  help  him  to  solve 
his  problems;  that  his  systematic  methods  of  going  at  a 
thing  help  him  to  do  his  work  more  easily  and  quickly; 
that  by  following  the  dry  old  laws  of  logic,  his  conclusions 
are  somehow  better  than  those  of  the  other  fellow  who  does 
not  take  the  trouble  to  see  that  all  the  steps  in  the  prob- 
lem are  "  necessary  and  sufficient."  In  short,  he  comes  to 
realize  that  his  education  has  enabled  him  to  do  his  work 
easier  and  better  and  has  given  him  intellectual  confidence. 
If  it  doesn't  do  this  for  him  he  has  wasted  his  opportunities 
in  college. 

436 


MILITARY '  STATISTICS  437 

In  the  preceding  chapters  of  this  book  the  author  has  en- 
deavored to  place  the  emphasis  not  on  the  subject  matter 
i  but  on  methods  of  procedure,  to  outline  the  simpler  prin- 
ciples of  the  statistical  method  as  applied  to  studies  in 
|  demography,  to  warn  against  the  common  fallacies  which 
i  so  often  creep  into  discussions  of  vital  statistics,  and  to  urge 
students  and  health  officers  not  to  be  content  with  such 
things  as  general  rates  but  to  seek  the  answers  to  their'prob- 
lems  by  methods  of  statistical  analysis  and  the  use  of  specific 
rates  and  ratios. 

Let  us  now  take  an  outlook  upon  some  of  the  problems 
;  of  demography  as  they  come  piling  in  upon  the  health  officer 
i  from  day  to  day.  And  if,  for  convenience'  sake,  we  take 
them  at  random,  one  after  the  other,  without  order  or  system 
we  shall  simulate  more  nearly  every-day  practice.  If  we 
can  solve  this  and  that  problem  or  if  we  can  see  the  steps 
in  the  solution  we  shall  know  that  we  have  acquired  the 
use  of  the  tools  of  the  statistician,  and  will  have  confidence 
in  our  own  studies.  This  chapter  will  also  include  certain 
subjects  which  have  not  logically  found  a  place  in  the  pre- 
ceding chapters.  Several  of  these  subjects  might  easily  be 
expanded  into  chapters  of  their  own. 

Military  statistics.  —  In  general  the  vital  statistics  of 
•armies  are  computed  in  the  same  way  as  those  of  civil  pop- 
ulations, but  instead  of  using  the  mid-year  estimated 
population,  the  mean  strength  for  the  year  is  used  as  a 
I  basis  of  rates.  An  army  does  not  increase  in  numbers  as  a 
population  grows,  slowly  by  geometrical  progression,  but 
is  kept  up  to  a  fairly  constant  strength  or  is  suddenly 
increased  or  decreased  according  to  demands  made  upon  it. 
An  army  represents  a  selected  population,  —  males  be- 
tween certain  age  limits,  and  above  set  standards  of  health 
and  physique.  Rates  computed  for  armies  are  therefore 
specific  rates  and  they  must  not  be  compared  with  general 


438  A  COMMENCEMENT  CHAPTER 

rates.  The  health  of  the  soldiers  is  carefully  looked  after 
by  the  surgeons,  who  are  obliged  to  keep  records;  hence 
the  morbidity  records  are  more  complete  than  in  the  case 
of  the  civil  population. 

Since  1894,  when  an  international  commission  for  the  uni- 
fication of  medical  statistics  met  at  Budapest,  tables  of 
statistics  made  up  according  to  certain  schedules  have  been 
published  for  most  armies.  These  may  be  found  in  the 
annual  reports  of  the  Surgeon  General  of  the  U.  S.  A.  In 
the  report  for  1916  we  find  that  in  the  entire  U.  S.  army 
of  93,262  enlisted  men  in  1915  the  sick  admissions  "  to  quar- 
ters "  and  "  to  hospitals "  amounted  to  745  per  1000. 
This  does  not  mean  745  different  men,  for  sometimes  the 
same  man  was  admitted  more  than  once.  Of  these  96  per 
cent  returned  to  duty,  i.e.  recovered,  0.65  per  cent  died, 
and  3.4  per  cent  were  "  otherwise  disposed  of."  The 
death-rate  for  the  mean  strength  was  4.6  per  1000.  The 
annual  number  of  days  lost  through  sickness  was  9.44  for 
each  soldier,  or  12.7  for  each  "  admission."  In  the  pub- 
lished tables  the  figures  are  classified  according  to  the 
location  of  the  troups,  the  arms  of  the  service,  the  season, 
the  larger  garrisons,  and  according  to  the  cause  of  the  sick- 
ness or  death.  It  should  be  observed  that  in  the  interna- 
tional tables  for  the  army  the  international  list  of  diseases/ 
as  given  on  page  257,  is  not  followed.  The  Surgeon  General 
of  the  United  States  uses  it,  however,  in  the  body  of  his 
report. 

In  1915  in  the  entire  U.  S.  army  (103,842  officers  and 
enlisted  men)  the  following  were  the  rates  per  1000  of 
mean  strength: 


MILITARY  STATISTICS 


439 


TABLE  149 
VITAL  STATISTICS  OF  U.  S.  ARMY:    1915 


Death-ratea  per  1000. 

From  disease. 

From  injury. 

Total. 

(1) 

(2) 

(3) 

(4) 

Admissions 

597.0 

12.6 
2.5 
15.1 

129.2 

1.4 
1.9 
3.3 

726.2 

14.0 
4.4 
18.4 

Discharged  on  certificate  of 
disability  

Died 

Total  losses 

The  percentage  of  soldiers  constantly  non-effective  was 
2.5  per  cent. 

If  we  look  back  a  few  years  we  find  that  the  health  of 
the  army  has  been  improving. 


TABLE  150 

HOSPITAL  ADMISSION  RATES  AND  PERCENTAGE 
OF  NON-EFFECTIVES,   U.  S.  A. 


Year. 

Admission-rate 
per  1000 

Non-effectives, 
per  cent. 

(1) 

(2) 

(3) 

1906 

1118 

4.8 

1907 

1102 

4.4 

1908 

1079 

4.2 

1909 

964 

4.1 

1910 

870 

3  5 

1911 

858 

3.2 

1912 

806 

2.9 

1913 

666 

2.4 

1914 

660 

2.4 

1915 

726 

2.5 

1916 

597 

2.5 

440  A  COMMENCEMENT  CHAPTER 

Army  diseases.  —  In  the  consideration  of  army  diseases 
one  must  distinguish  between  peace  times  and  war  times; 
one  must  also  distinguish  between  the  diseases  which  cause 
death  and  those  which  render  the  men  non-effective. 

In  1915  the  specific  death-rates  among  the  American 
enlisted  men  in  the  U.  S.  A.  were,  in  order  of  their  im- 
portance, as  follows: 

Per  100,000 

Tuberculosis 33 

.    Pneumonia  (lobar) 31 

Organic  heart  disease 23 

Measles 23 

Appendicitis 13 

Epidemic  cerebro-spinal  meningitis 11 

The  principal  causes  of  discharge  were : 

Per  1000 

Mental  alienation 3.30 

Tuberculosis 1.79 

Flat  foot 1.25 

Venereal  disease 0.82 

Epilepsy 0.69 

Organic  heart  disease 0.50 

The  admission  and  non-effective  rates  for  white  enlisted 
men  were: 


ARMY  DISEASES 


441 


TABLE  151 

ADMISSION  RATES  AND'  PERCENTAGE  OF  NON-EFFECTIVES 
FROM  PARTICULAR  DISEASES,  U.  S.  A. 


Admission  rate, 
per  1000 

Non-effectives, 
per  cent. 

(1) 

(2) 

(3) 

Venereal  diseases  

106 

0  47 

Tuberculosis  

3 

0  17 

Mental  alienation  
Bronchitis  

4 
35      . 

0.09 
0  06 

Tonsilitis 

47 

0  07 

Appendicitis 

9 

0  06 

Malaria 

24 

0  05 

Mumps 

10 

0  05 

Influenza 

35 

0  05 

Diarrhoea  and  enteritis   .  . 

32 

0  04 

Measles 

7 

0  05 

Articular  rheumatism     .  .    .     

6 

0  04 

Hernia  

4 

0.04 

In  war  times  we  have  to  consider  the  venereal  diseases, 
syphilis,  gonorrhoea,  etc.;  the  diarrhoeal  diseases,  typhoid 
fever,  cholera,  dysentery;  the  insect-borne  diseases,  typhus 
fever,  relapsing  fever,  trench  fever,  malaria,  etc.;  scurvy  — 
besides  all  sorts  of  diseases  associated  with  wounds.  No 
attempt  will  be  made  here  to  discuss  these  war  diseases, 
because  the  Great  War  will  yield  statistics  better  and 
more  complete  than  any  which  we  now  have.  Some  day 
it  will  be  in  order  to  make  comparisons  between  the 
Civil  war,  the  Spanish  war  and  the  present  Great  War. 
We  shall  then  see  what  enormous  strides  have  been  taken 
in  sanitation,  in  the  use  of  antitoxins,  in  providing  proper 
food,  in  the  enforcement  of  the  rules  of  personal  hygiene, 
in  the  treatme'nt  of  the  sick  and  wounded,  in  the  ambulance 
and  hospital  service,  in  the  protection  of  the  health  of  the 
civil  population  in  war  time  in  factory  and  home.  One 


442  A  COMMENCEMENT  CHAPTER 

gratifying  result  of  the  war  seems  assured  —  a  world-wide 
up-lift  in  public  health.  We  shall  hereafter  need  world- 
wide vital  statistics,  that  is,  we  shall  need  the  science  of 
demography. 

.  Effect  of  the  Great  War  on  demography.  —  A  thousand 
and  one  questions  have  arisen  as  a  result  of  the  war. 

What  are  we  to  do  with  the  enormous  number  of  non- 
resident males  in  the  United  States?  How  are  we  to 
compute  death-rates?  Will  our  usual  methods  have  to 
be  modified  as  an  emergency  measure? 

What  effect  has  the  war  had  on  the  marriage-rates, 
birth-rates  and  death-rates?  A  big  hole  is  sure  to  be  made 
in  the  male  population  for  the  ages  of  youth  and  early 
manhood;  fewer  young  men  of  twenty  in  1920  will  mean 
fewer  men  of  thirty  in  1930  and  fewer  men  of  forty  in 
1940.  How  will  this  alter  the  general  death-rate?  Will 
the  birth-rate  rise  as  a  natural  reaction  to  war's  destruction 
or  will  hard  economic  conditions  keep  it  low?  Can  we  learn 
anything  from  past  wars  on  this  matter? 

Typhoid  fever,  the  past  scourge  of  armies,  has  been  al- 
most completely  conquered.  Will  the  venereal  diseases 
also  be  conquered?  Will  the  Great  War  point  out  the  way 
to  this  end? 

What  has  been  the  effect  of  reduced  food  rations  on  health 
and  physique?  Will  the  loss  of  the  most  vigorous  young 
men  lower  the  standards  of  physique  by  hereditary  in- 
fluences? 

Will  the  lessons  in  hygiene  and  sanitation  be  so  well  learned 
that  their  benefits  will  offset  other  baneful  influences? 

We  knew  approximately  the  standing  of  the  nations 
before  the  war  as  to  population,  natural  rates  of  growth, 
migrations,  death-rates,  and  so  on  —  how  will  these  nations 
stand  after  the  war?  Who  will  be  the  greatest  losers? 
What  will  be  their  most  serious  losses? 


STATISTICS  OF  INDUSTRIAL  DISEASE  443 

Such  questions  as  these  force  themselves  upon  us.  Demog- 
raphy will  be  the  science  looked  to  for  the  answers. 

Hospital  statistics.  —  There  are  many  hospitals  in  the 
country  and  they  are  an  increasingly  important  factor  in 
the  control  of  disease.  Some  of  these  hospitals  keep  good 
records  of  their  cases  and  some  publish  them.  Other  hos- 
pitals keep  very  inadequate  records  and  publish  nothing. 
Uniformity  in  this  matter  is  most  desirable,  as  a  good  op- 
portunity for  collecting  facts  in  regard  to  certain  non- 
reportable  diseases  and  in  regard  to  the  fatality  of  these 
diseases  is  being  lost. 

Several  plans  for  unifying  hospital  statistics  have  been 
suggested.  Dr.  Charles  F.  Bolduan,1  of  the  New  York 
i  City  Health  Department,  suggested  the  idea  of  a  dis- 
charge certificate,  to  be  filled  out  for  each  case  on  leaving 
a  hospital,. —  a  certificate  comparable  to  the  ordinary  death 
certificate.  Another  method  is  to  have  the  annual  re- 
ports (or  monthly  reports)  made  out  on  some  fixed  schedule 
of  statistics  and  submitted  to  some  central  authority.2 
Perhaps  the  U.  S.  Public  Health  Service  may  some  day 
take  the  lead  in  the  collection  of  the  important  data  to  be 
secured  from  hospitals.  See  also  page  471. 

Statistics  of  industrial  disease.  —  Statistical  studies  of 
industrial  diseases  are  becoming  increasingly  numerous. 
It  is  a  most  complex  and  difficult  branch  of  the  subject. 
At  the  outset  we  are  met  with  the  fundamental  difficulty  of 
defining  occupations.  The  extent  of  this  difficulty  may  be 
appreciated  from  the  fact  that  in  1915  the  U.  S.  Bureau  of  the 
Census  published  an  "  Index  to  Occupations"  which  covered 
over  four  hundred  pages  and  included  9000  occupational  des- 
ignations. The  report  makes  215  main  classes,  84  of  which 
are  subdivided.  This  list  has  been  given  in  Chapter  VIII. 

1  N.  Y.  Medical  Journal,  Mar.  29,  1913. 

2  Amer.  Jour.  Pub.  Health,  Apr.,  1918. 


444 


A  COMMENCEMENT  CHAPTER 


A  second  difficulty  is  due  to  the  migration  of  laborers 
from  place  to  place,  and  from  one  class  to  another.  A 
third,  which  grows  out  of  the  other  two,  is  the  difficulty  of 
getting  constant,  well-defined  classes  to  serve  as  the  basis 
of  the  computation  of  rates  and  ratios.  A  fourth  is  the 
oft  repeated  error  of  concealed  classification.  These  and 
other  minor  difficulties  have  compelled  us  to  resort  to 
the  use  of  specially  gathered  statistics,  which  are  often  not 
truly  representative  of  the  conditions  discussed. 

For  example,  the  Massachusetts  General  Hospital  re- 
cently made  a  study  of  lead  poisoning  in  its  Industrial 
Clinic.  During  the  first  year  of  this  clinic  148  cases  of 
lead  poisoning  were  diagnosed  in  the  hospital  as  against 
147  during  the  previous  five  years. 

This  was  found  by  sifting  out  of  the  hospital  admissions 
by  a  trained  worker  those  suspected  of  being  exposed  to 
special  industrial  hazard.  A  study  of  these  148  cases  gave 
an  industrial  distribution  as  follows: 


TABLE   152 


Occupation. 

Number 
exposed. 

Number 
casea. 

Per  cent 
poisoned. 

(1) 

(2) 

(3) 

(4) 

Painters  

217 

68 

31 

House  

56 

Others. 

12 

Shipyard  and  navy  yard 

54 

16 

30 

Rubber  workers 

169 

11 

7 

Brass  foundrymen  

9 

4 

44 

Lead  and  lead  oxide  worker.  .  .  . 

6 

Plumbers  

42 

8 

19 

Printers 

64 

11 

17 

Miscellaneous 

135 

14 

10 

Non-industrial  

10 

Total 

148 

ECONOMIC  CONDITIONS  AND  HEALTH  445 

An  attempt  to  ascertain  the  rate  of  attack  was  made  by 
ascertaining  as  well  as  possible  the  number  of  persons 
exposed.  These  rates  are,  of  course,  far  too  high ;  31  per  cent 
of  all  painters  did  not  get  lead  poisoning,  but  only  31  per  cent 
of  the  exposed  persons  who  were  sorted  out  in  this  indus- 
trial clinic.  The  report  does  not  err  in  this  respect  but  the 
reader  may  get  a  false  impression  unless  he  reads  thought- 
fully. The  underlying  idea  of  this  clinic  is  excellent  and 
the  work,  unfortunately  interrupted,  was  already  yielding 
excellent  results.  The  danger  of  lead  poisoning  of  men 
engaged  in  certain  occupations  in  ship  yards  was  clearly 
shown. 

Economic  conditions  and  health.  —  Poverty  and  disease 
mutually  influence  each  other.  We  cannot  expect  to 
solve  the  problem  by  attacking  either  alone.  It  is  most 
difficult  to  separate  cause  from  effect.  In  fact,  there  is  a 
third  major  .factor  which  we  may  call  ignorance  —  and 
all  three  are  mutually  dependent.  Then  there  are  many 
minor  factors. 

We  can  correlate  these  things  by  statistics,  and  that  is 
worth  while  because  it  calls  attention  to  the  problems; 
but  the  plan  of  attack  must  rest  upon  the  fact  that  the 
different  conditions  are  mutually  related.  If  we  help  only 
a  little  to  raise  the  economic  and  hygienic  conditions 
the  result  is  an  accelerating  social  advance;  to  aid  one 
without  the  other  does  not  bring  about  permanent 
betterment. 

A  glimpse  at  these  mutual  relations,  as  shown  by 
Warren  and  Sydenstricker,1  is  instructive.  They  classified 
the  health  of  certain  garment  workers  with  respect  to  the 
annual  earnings  of  the  heads  of  families  as  follows: 

1  Pub.  Health  Reports,  May  26,  1916,  p,  1298. 


446 


A  COMMENCEMENT  CHAPTER 


TABLE  153 
HEALTH  OF  GARMENT  WORKERS 


Annual  earnings. 

$500 

$500-$699 

$700 

(1) 

(2) 

(3) 

(4) 

Number  of  persons  

381 

581 

462 

Ave.  annual  earnings.  .  

$382 

$577 

$866 

Ave  rate  of  weekly  earnings  

$19 

$23 

$27 

Per  cent  which  actual  earnings  were  of 

maximum  possible  earnings  
Maximum  possible  earnings  for  year  .  .  . 

38% 
$988 

48% 
$1196 

61% 
$1404 

Ave.  number  of  persons  per  family  

5.36 

5.38 

4.88 

Ave.  number  of  children  born  per  family 
Ave.    number   of  children  living  per 

3.78 

3.34 

2.75 

family 

2  99 

2  78 

2  43 

Ave.  number  of  children  dead  per  family 

0.78 

0.56 

0.32 

Infant  mortality  rate.  .    . 

206  9 

167  2 

116.5 

Per   cent    of   male    married    garment 

workers  who  were  poorly  nourished.  . 
Ave.  haemoglobin  index,  Talquist  

25.00 
85.94 

15.02 
86.99 

12.72 
87.35 

Per  cent  with  haemoglobin  index  under 

80 

9  94 

5  65 

4  42 

Per  cent  of  family  heads  tuberculous.  .  . 

5.64 

5.30 

0.44 

Accidents  and  accident-rates.  —  Injuries  and  deaths 
from  accidental  causes  are  attracting  much  attention 
nowadays,  and  rightly  so.  The  death-rate  from  accidents 
in  the  United  States  is  far  greater  than  from  typhoid  fever. 
Only  a  few  years  ago  it  was  more  than  100  per  100,000  of 
population.  Some  of  the  principal  causes  are  railroad 
accidents,  falls,  drowning  and  burns,  but  there  are  many 
accidents  associated  with  different  industries.  All  of 
these  present  interesting  problems  for  study  and  each 
should  be  studied  by  itself. 

Taking  accidents  as  a  general  class,  we  find  that  the 


ACCIDENTS  AND  ACCIDENT-RATES  447 

specific  death-rates  follow  closely  the  death-rates  from  all 
causes,  decreasing  from  the  first  year  to  a  minimum  be- 
tween ages  10-14  and  then  increasing  steadily  to  the 
highest  ages.  Owing  to  the  age  distribution  of  population 

;  we  find  the  mode  of  the  accident  distribution  curve  occur- 
ring somewhere  in  age  group  25-29  years. 

In  the  case  of  railroad  accidents  among  males  the  mode 
is  found  in  age-group  25-29  years,  that  is,  the  largest 
number  of  accidents  occurs  among  males  at  that  period; 
in  the  case  of  falls  the  mode  is  in  age-group  45^19;  in  the 
case  of  drowning  it  is  at  age  20-24.  The  specific  death-rate 
from  railroad  accidents  is  low  until  the  age  of  twenty,  when 

:  it  rises  to  above  30  per  100,000  and  fluctuates  between  30 
and  50  for  all  higher  age-groups.     The  specific  death-rate 

,  from  falls  rises  steadily  from  the  tenth  year  and  above  75 
years  of  age  exceeds  100  per  100,000.  The  specific  death- 
rate  from  drowning  on  the  other  hand  is  highest  at  about 
twenty  years  of  age.  Except  for  falls  the  accident-rates 
from  the  major  causes  are  higher  for  males  than  for  females. 
If  time  permitted  it  would  be  interesting  to  follow  up  this 
subject  of  accidents  and  find  the  seasonal  distribution  and 

•  classify  them  in  other  ways. 

In  studying  accidents  in  industrial  establishments  we 
must  ask  the  usual  questions,  —  where,  when,  what,  how, 
who,  and  answer  them  by  collecting  the  necessary  statistics. 
It  does  not  do  to  follow  popular  impressions  in  these  mat- 
ters. Thus  it  is  sometimes  said  that  most  accidents  occur 
"  at  the  end  of  a  tired  day,"  yet  statistics  collected  in  Massa- 
chusetts by  the  Industrial  Accident  Board  showed  that  it  is 
between  9  and  10  A.M.  and  2  and  3  P.M.  that  accidents  are 
most  frequent.  Yet  this  general  statement  is  not  enough. 
We  need  to  know  what  kinds  of  accidents  are  meant.  Per- 
haps some  kinds  of  accidents  do  occur  at  the  end  of  the 
working  day.  Then  there  are  daily  differences  to  be  con- 


448  A  COMMENCEMENT  CHAPTER 

sidered,  and  seasonal  differences,  as  well  as  differences  due 
to  the  weather.  In  the  case  of  the  English  munition  fac- 
tories, which  run  night  and  day,  the  accident  mode  occurs 
in  the  evening.  One  runs  a  great  risk  in  generalizing  from 
composite  statistics. 

There  are  various  ways  of  expressing  accident  rates. 
One  is  the  ratio  between  annual  accidents  and  number  of 
employees.  Another  is  between  annual  accidents  and  the 
number  of  full  time  workers,  i.e.,  300  days  per  year. 
Another  is  between  days  lost  through  accident  and  full 
time  workers.  Differences  in  the  severity  of  the  accidents 
are  also  important  from  an  economic  point  of  view. 

Age  distribution  of  cases  of  poliomyelitis.  —  One  of  the 
diseases  which  has  recently  attracted  attention  is  Anterior 
Poliomyelitis,  commonly  known  as  infantile  paralysis. 
Many  attempts  have  been  made  to  correlate  the  occur- 
rences of  this  disease  with  factors  which  might  point  to 
the  manner  of  its  communic ability.  There  is  an  excellent 
opportunity  here  for  original  statistical  work  based  on  re- 
cently accumulated  data.  As  bearing  on  the  theory  of 
contact  as  a  major  element  in  its  communicability  the 
age  distribution  of  the  cases  is  important.  The  disease  is 
essentially  o'ne  of  the  early  ages.  A  recent  study  by  the 
author  appears  to  indicate  that  the  median  age  is  inversely 
proportional  to  the  density  of  population.  This  is  like- 
wise true  for  measles,  whooping  cough  and  similar  diseases. 

It  has  been  noticed  that  if  the  cases  of  poliomyelitis  are 
plotted  on  logarithmic  probability  paper  they  tend  to  fall 
on  a  straight  line,  except  that  above  the  upper  decentile 
there  is  an  irregular  divergence  from  the  straight  line. 
From  this  diagram  it  is  easy  to  read  off  the  median  age 
or  the  per  cent  of  cases  below  any  age  or  between  given 
ages.  Fig.  63  shows  that  in  the  populous  city  of  New 
York  the  median  age  was  2.5  years,  in  Boston  3.7  years, 


AGE  DISTRIBUTION  OF  CASES  OF  POLIOMYELITIS     449 


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450  A  COMMENCEMENT  CHAPTER 

and  in  Minnesota  4.6  years.  Similar  differences  were 
observed  in  the  upper  decentiles.  These  data  are  not 
strictly  comparable  as  they  were  not  for  the  same  year  and 
are  presented  merely  to  show  the  advantage  of  this  method 
of  plotting.  It  is  interesting  to  note  that  scarlet  fever 
cases  plotted  by  ages  on  logarithmic  probability  paper  also 
fall  nearly  on  a  straight  line. 

The  Mills-Reincke  Phenomenon.  —  Problems  like  this 
offer  excellent  opportunities  to  apply  the  principles  of 
statistics.  In  1893-94  Mr.  Hiram  F.  Mills  found  that  at 
Lawrence,  Mass.,  after  the  introduction  of  the  sand  filter  to 
purify  the  public  water-supply  taken  from  the  polluted 
Merrimac  River,  there  was  a  material  reduction  in  the 
general  death-rate  of  the  city.  Notably  typhoid  fever  was 
reduced,  but  this  reduction  was  not  sufficient  to  account 
for  the  fall  in  the  general  death-rate.  About  the  same 
time  Dr.  J.  J.  Reincke  found  the  same  thing  in  Hamburg. 
In  1904  Hazen  studied  these  and  other  records  and  stated 
that  "  where  one  death  from  typhoid  fever  had  been  avoided 
by  the  use  of  better  water,  a  certain  number  of  deaths, 
probably  two  or  three,  from  other  causes  have  been 
avoided."  In  1910  Sedgwick  and  MacNutt l  published  an 
elaborate  study  in  which  Hazen's  statement  was  dignified 
with  the  rank  of  ''theorem." 

The  natural  inference  from  such  statements  is  that  the 
purification  of  a  polluted  water-supply  reduces  deaths  from 
causes  other  than  typhoid  fever.  In  Lawrence  if  one  con- 
siders short  periods  before  and  after  the  introduction  of  the 
filter  a  decrease  is  observed  in  several  diseases,  —  as,  for 
example,  pneumonia,  tuberculosis,  cholera  infantum  and  so 
on.  Some  have,  without  sufficient  thought,  extended  the 

1  Sedgwick,  W.  T.  and  J.  Scott  MacNutt.  On  the  Mills-Reincke 
Phenomenon  and  Hazen's  Theorem.  Jour.  Infectious  Diseases,  Aug., 
1910,  pp.  489-564. 


THE  SANITARY  INDEX  451 

idea  back  of  Hazen's  "  theorem  "  to  undue  limits,  and  have 
argued  that  pure  water  has  the  effect  of  raising  the  gen- 
eral health,  of  lifting  the  health  tone  of  individuals,  and  so 
has  a  value  beyond  that  of  preventing  the  spread  of  diseases 
of  the  intestinal  tract.  This  is  unwarranted  and  to  that 
extent  Dr.  Chapin  l  has  rightly  criticized  the  "  theorem." 
The  idea  may  be  correct,  but  the  vital  statistics  available 
do  not  demonstrate  it.  The  correlation  between  the  de- 
creased typhoid-fever  rate  and  the  general  death-rate  in 
cities  which  have  introduced  water  filtration  or  otherwise 
bettered  their  supply  is  not  high.  It  is  more  frequently-true 
where  the  original  water-supply  has  been  very  badly  pol- 
luted, as  was  the  case  at  Lawrence.  Even  at  Lawrence  it  is 
probable  that  the  pneumonia  death-rate  was  abnormally 
high  just  before  the  filter  was  built  and  that  the  reason 
for  its  subsequent  decrease  had  little  or  nothing  to  do  with 
water ^  filtration.  Yet  to  condemn  the  "  theorem  "  al- 
together is  to  take  too  extreme  a  view.  Without  doubt 
infant  mortality  was  reduced  by  filtration,  chiefly  through 
the  reduction  in  diarrhceal  diseases.  McLaughlin  has 
shown  that  this  has  occurred  in  many  places. 

The  trouble  with  this  whole  problem  has  grown  out  of 
the  use  of  general  rates.  If  we  want  to  find  the  effect  of 
filtration  we  must  compare  the  morbidity  and  mortality 
rates  for  particular  diseases  before  and  after  filtration,  with 
due  regard  to  changes  in  population.  Somebody  who  has 
time  ought  to  restudy  this  whole  matter  in  the  light  of 
recent  data. 

The  sanitary  index.  —  Many  attempts  have  been  made 
to  devise  a  "  sanitary  index,"  to  select  and  combine  certain 
specific  death-rates  so  as  to  get  for  a  given  place  a  single 
figure  which,  when  compared  with  similar  figures  for  other 
places,  will  correlate  health  and  sanitary  conditions.  We 
1  Chapin,  Chas.  V.,  "Modes  of  Infection." 


452  A  COMMENCEMENT  CHAPTER 

know  that  the  general  death-rate  will  not  serve  this  pur- 
pose. Even  the  death-rate  adjusted  to  a  standard  popu- 
lation is  inadequate.  The  infant  mortality  has  been 
claimed  as  the  best  index.  Dr.  Wilmer  R.  Batt,1  the 
Registrar  of  the  Pennsylvania  State  Department  of  Health, 
has  suggested  a  composite  index  which  illustrates  this 
striving  to  get  an  index.  It  is  computed  as  follows: 

Sanitary  index  = 

Deaths  from  causes  No.  1  to  No.  15  plus  all  infant  deaths 
Population 

The  ratio  of  all  the  other  deaths  to  the  population  is 
called  the  residual  death-rate.  Hence  the  sum  of  the  two 
gives  the  general  death-rate. 

He  found  that  from  1906  to  1915  the  general  death-rate 
of  the  state  declined  from  16.0  to  13.8  per  1000  i.e.,  13.8 
per  cent.  The  "  sanitary  index,"  however,  declined  from 
6.5  to  4.5,  or  30.8  per  cent,  while  the  residual  death-rate 
declined  from  9.5  to  9.3  or  only  2.1  per  cent.  This  index, 
it  will  be  observed,  takes  no  account  of  the  changing  com- 
position of  the  population. 

Others  have  suggested  that  the  index  ought  to  be  based 
on  social  and  economic  factors  as  well  as  vital  statistics, 
and  their  point  seems  to  be  well '  taken.  This  only  em- 
phasizes the  complexity  of  the  problem.  The  author  be- 
lieves that  it  is  too  early  to  attempt  the  establishment  of 
a  health  index,  and  that  better  results  will  be  secured  by 
the  critical  use  of  specific  rates. 

Current  use  of  vital  statistics.  —  Vital  statistics  have 
their  historic  uses,  but  their  greatest  value  lies  in  their 
immediate  use.  It  is  interesting  and  ultimately  most  val- 
uable to  know  that  a  baby  has  been  born  at  a  certain  place, 
on  a  certain  day,  of  such  and  such  parentage,  but  it  is  more 
1  Penn.  Monthly  Health  Bulletin,  No.  70,  Feb.,  1916. 


CURRENT  USE  OF  VITAL  STATISTICS  453 

important  that  the  baby  shall  live  and  grow  up  well.  No 
baby  should  be  allowed  to  come  unnoticed  into  the  world; 
boards  of  health  or  other  proper  authorities  should  see  to  it 
that  every  baby  born  has  a  good  chance  to  live.  In  most 
cases  the  parents,  the  physician  and  the  nurse  are  sufficient 
caretakers  and  the  public  authorities  should  not  be  un- 
necessarily intrusive  or  over-zealous;  on  the  other  hand 
their  advice  and  aid  should  be  prompt  where  occasion  war- 
rants, and  immediate  knowledge  of  the  facts  is  the  only 
basis  of  wise  action. 

In  reported  cases  of  diseases  dangerous  to  the  public 
health  the  need  for  prompt  action  is  even  greater.  It 
is  by  the  daily  study  of  such  reports  that  pending  epi- 
demics or  local  outbreaks  of  disease  may  be  headed  off. 
Every  local  health  officer  should  keep  on  the  walls  of  his 
office,  or  on  a  suitable  frame,  or  in  shallow  drawers,  a  series 
of  local  maps  —  one  for  each  important  communicable  dis- 
ease. The  maps  should  show  the  names  of  the  streets. 
There  should  be  a  street  index  at  hand,  with  the  street 
numbers  given  for  each  intersection,  and  with  information 
as  to  which  side  of  the  street  has  the  odd  (or  even)  numbers. 
On  these  maps,  with  the  aid  of  the  index,  each  case  of 
communicable  disease  should  be  marked  with  a  pin  imme- 
diately on  receipt  of  the  report.  There  are  many  little 
devices  involving  the  use  of  pins  of  different  colors  for 
different  dates,  the  removal  of  pins  after  recovery,  the  ad- 
ditions of  pins  to  indicate  death,  and  so  on;  the  details  of 
which  are  bound  to  vary  according  to  local  conditions. 
But  the  main  thing  is  to  study  the  pins  daily.  In  the  case 
of  state  departments  of  health  the  required  maps  are  of 
course  on  a  different  scale  and  the  cases  are  arranged  by 
cities  and  towns  instead  of  streets.  Both  local  and  state 
studies  are  necessary. 

In  addition  to  the  location  maps  the  health  officer  needs 


454  A  COMMENCEMENT  CHAPTER 

to  keep  up  chronological  charts  for  each  disease  —  a 
separate  chart  for  each.  Pins  may  be  used  for  this  work 
also,  or  lines  may  be  drawn,  black  or  colored.  These 
charts,  together  with  the  maps,  answer  the  questions 
where  and  when  did  the  cases  occur. 

For  state  work  another  device  is  convenient,  —  namely, 
a  summary  of  cases  by  cities,  towns,  or  other  geographical 
divisions,  and  by  weeks  or  months.  These  should  be  made 
up  regularly  for  comparison  with  past  records.  All  cities 
have  certain  numbers  of  cases  of  communicable  diseases 
which  occur  with  a  fair  degree  of  regularity  —  and  what 
the  health  officer  needs  most  to  know  is  whether  there  is  at 
any  time  an  abnormally  large  number  of  cases  of  any  dis- 
ease. In  order  to  quickly  tell  this  he  needs  to  have  at 
hand  certain  generalized  results  of  past  experience.  In 
New  York  City  Dr.  Bolduan  has  been  in  the  habit  of  find- 
ing the  average  number  of  cases  of  typhoid  fever,  for  ex- 
ample, in  each  ward  and  for  each  week  of  the  year,  —  but 
omits  from  these  averages  any  local  outbreak  or  epidemics. 
He  has  called  this  the  "  normalized  average."  l  In  the 
author's  opinion  what  is  needed  here  is  not  the  average, 
with  the  unusual  conditions  omitted,  but  the  median. 
The  Massachusetts  State  Department  of  Health  is  using 
the  median  under  the  name  of  the  "  endemic  index."  A 
better  name  would  be  the  endemic  median.  This  can  be 
very  easily  found  for  a  five-  or  ten-year  period  and  would 
serve  admirably  as  a  standard  of  comparison.  It  would 
of  course  need  occasional  revision. 

Card  systems  are  generally  found  most  convenient  for 
keeping  records  of  individual  reports,  and  the  punched- 
card  system  with  mechanical  devices  for  sorting  and  count- 
ing is  the  best  of  all. 

1  Bolduan,  Chas.  F.t  Typhoid  Fever  in  New  York  City,  No.  3 
Monograph  Series,  Aug.,  1912. 


PUBLICATION  OF  REPORTS  455 

Publication  of  reports.  —  The  author  will  perhaps  be 
regarded  as  a  heretic  on  the  subject  of  published  reports. 
He  believes,  however,  that  thousands  of  pages  of  useless 
tables  of  reported  cases  of  disease  are  printed  every  year  in 
the  United  States  at  enormous  expense  and  that  the  same 
amount  of  money  spent  in  maintaining  more  complete  and 
more  accurate  records  in  state  and  local  health  departments 
and  in  studying  and  using  the  records  from  day  to  day 
would  bring  better  results.  The  object  of  reporting  dis- 
eases dangerous  to  the  public  health  is  not  to  pile  up 
records  but  to  prevent  the  diseases  from  spreading.  State- 
ments of  the  occurrences  of  communicable  diseases  pub- 
lished monthly,  or  even  weekly,  usually  reach  their  readers 
too  late  to  be  of  any  practical  use,  while  as  historical 
records  such  frequent  publication  is  wholly  unnecessary. 
Some  publication  is  desirable,  however,  but  only  that  which 
is  of  real  use. 

Let  us  consider  the  case  of  communicable  diseases,  for 
example,  as  reported  to  a  state  department  of  health.  If 
the  number  of  cases  of  measles  in  a  city  is  less  than  the 
endemic  median,  that  is,  less  than  the  ordinary  number 
of  cases,  no  announcement  is  necessary;  but  should  the 
number  of  cases  rise  above  the  endemic  median  a  prompt 
announcement  of  that  fact  in  the  local  paper  1  might  be 
of  positive  benefit  as  it  would  sound  a  warning.  If  the 
fire  bells  were  ringing  very  gently  all  the  time  except  when 
a  fire  occurred  and  then  rang  loudly,  the  public  would  not 
i  heed  the  warning;  and  in  the  same  way  the  constant  pub- 
lication of  figures  which  are  of  little  moment  blunts  the 
sense  of  caution.  Arrangements  might  well  be  made,  how- 
ever, for  the  immediate  publication  of  notices  of  all  unusual 
occurrences  of  disease  in  local  papers  or  wherever  such 
notices  would  do  the  most  good.  So  far  as  communicable 
1  Daily  paper  preferred, 


456  A  COMMENCEMENT  CHAPTER 

diseases  are  concerned  the  general  principle  of  publication 
should  be  to  publish  at  once  or  not  at  all  and  to  publish 
only  the  unusual  occurrences.  The  preparation  of  such 
notices  would  by  reflex  action  stimulate  the  health  officers 
themselves,  and  would  assist  physicians  in  making  diagnosis 
of  suspected  cases. 

The  problem  of  annual  reports  is  different.  Here  the 
object  is  to  establish  a  record  for  permanent  preservation, 
useful  alike  to  health  officers,  to  physicians,  and  to  the  in- 
terested public.  The  calendar  year  with  its  subdivisions 
is  the  most  convenient  unit  of  time.  The  vital  statistics 
of  every  political  subdivision  in  the  country  should  be 
published  annually,  and  as  soon  after  the  end  of  the  year 
as  possible.  Here  we  find  a  great  amount  of  unnecessary 
duplication.  It  is  a  waste  of  money  to  have  the  local 
Board  of  Health  of  Cambridge,  Mass.,  publish  certain  facts 
(usually  a  year  or  two  late),  to  have  the  same  facts  pub- 
lished by  the  State  Registrar  and  perhaps  by  the  State  De- 
partment of  Health,  and  finally  to  have  them  published 
again  by  the  U.  S.  Bureau  of  the  Census,  and  perhaps  by 
the  U.  S.  Public  Health  Service.  It  is  worse  than  waste- 
ful, because  the  various  tables  often  fail  to  agree  and  all 
sorts  of  distressing  statistical  errors  creep  in.  On  the  other 
hand,  while  the  figures  for  Cambridge  may  be  found  in 
several  places,  there  may  be  other  places  where  it  is  diffi- 
cult to  find  any  statistics  at  all.  Uniformity  in  this  matter 
is  very  greatly  needed,  and  this  must  come  through  federal 
control  or  state  cooperation,  with  uniform  minimum 
schedules  to  serve  as  a  basis  of  record. 

The  author  believes  that  no  systematic  attempt  should 
be  made  every  year  to  publish  specific  rates  or  minute 
analyses  of  rates,  for  the  reason  that  such  studies  are  based 
necessarily  on  estimated  populations.  Such  studies  are  of 
course  very  necessary  for  the  study  of  special  problems  as 


PUBLICATION  OF  REPORTS  457 

they  arise,  but  these  results  should  be  published  as  special 

studies  and  not  as  a  part  of  a  systematic  schedule.     It 

would  be  better  to  wait  for  the  census  years,  when  the 

facts  of  population  can  be  used  instead  of  estimates  and  to 

then  make  a  most  careful  analysis  of  all  vital  statistics. 

Such  an  analysis  made  once  in  five  years  in  Massachusetts 

would  serve  every  useful  purpose,  would  save  much  time 

and  expense,  would  avoid  the  need  of  revision  and  would 

prevent  the  publication  of  figures  which,  contain  annoying 

variations.     The  principle  should  be  to  wait  for  the  facts, 

I  and  then  make  a  careful  analysis  based  on  the  facts.     Of 

'  course,  general  rates  should  be  published  annually,  based 

)  on  estimated  populations,  but  no  one  need  take  these  very 

j  seriously,  as  in  any  event  they  mean  little.     If  it  is  thought 

'  worth  while  to  publish  specific  rates  for  each  post  censal 

year,  these  should  be  recomputed  after  the  next  census  has 

been  taken. 

Various  attempts  to  establish  standards  .have  been  made. 
One  of  these  may  be  found  in  the  American  Journal  of 
Public  Health.1  Another  in  the  annual  report  of  the  N.  Y. 
State  Department  of  Health  for  1912,  another  in  the 
Quarterly  Publication  of  the  American  Statistical  Associa- 
tion 2  and  so  on.  In  establishing  standards  it  will  be  neces- 
sary to  determine  what  shall  be  the  geographical  units, 
what  subdivision  of  the  year,  what  data  and  in  what  com- 
binations. The  usual  facts  secured  in  regard  to  deaths  are 
(1)  place  of  death,  (2)  time  of  death,  (3)  sex,  (4)  age, 
(5)  race  or  color,  (6)  cause  of  death,  (7)  birthplace,  (8) 
birthplace  of  father,  (9)  birthplace  of  mother,  (10)  marital 
condition,  (11)  occupation.  The  possible  number  of  com- 
binations of  these  eleven  items  two  at  a  time  is  55,  three  at 
a  time  165,  and  four  at  a  time  330.  No  wonder  therefore 
that  there  is  lack  of  uniformity  in  published  reports.  Any 
1  1913,  p.  595.  2  1911,  p.  510. 


458  A  COMMENCEMENT  CHAPTER 

standard  tables  must  of  necessity  be  arbitrary.  The  time 
has  come  when  uniformity  of  report  is  necessary  in  the  in- 
terest of  both  economy  and  efficiency. 

EXERCISES  AND    QUESTIONS 

1.  Distinguish  between  the  environments  represented  by  the  follow- 
ing terms: 

a.  A  felt  hat  and  a  straw  hat  factory. 

•  6.  A  paper  box  and  a  wooden  box  factory. 

c.  An  iron  and  a  brass  foundry. 

d.  A  wholesale  and  a  retail  merchant  or  dealer. 

e.  A  farm  laborer  on  his  home  farm  and  one  working  out. 
/.  A  clerk  in  a  store  and  a  salesman. 

g.  A  dressmaker  in  a  factory  or  shop  and  one  working  elsewhere. 

h.  A  cook  and  a  servant. 

i.  A  paid  housekeeper  and  a  servant  girl. 

j.  A  practical  and  a  trained  nurse. 

2.  To  what  extent  do  these  terms  conceal  other  important  differ- 
ences in  age  or  sex  or  nationality? 

3.  What  data  were  collected  in  the  industrial  clinic  of  the  Massa- 
chusetts  General  Hospital?     [Monthly  Review   (Dec.,  1917),   U.   S. 
Bureau  of  Labor  Statistics.    Edsall,  David  J. :  The  Study  of  Occupa- 
tional Diseases  in  Hospitals.] 

4.  How  would  you  explain  the  alleged  fact  that  more  cases  of  in- 
fectious diseases  are  reported  to  the  New  York  City  Department    of 
Health  on  Monday  than  on  any  other  day,  and  the  fewest  on  Saturday? 

5.  How  are  the  medical  and  .vital  statistics  of  the  U.  S.  Navy  kept? 
[See  Am.  J.  P.  H.,  June,  1918,  p.  442.] 

6.  How  are  the  medical  and  vital  statistics  of  the  U.  S.  army  kept? 
[See  Am.  J.  P.  H.,  Jan.,  1918,  p.  14.] 

7.  What  facts  are  needed  in  the  registration  of  still-births?     [See 
Am.  J.  P.  H.,  Jan.,  1917,  p.  46.] 

8.  Describe  the  epidemic  of  poliomyelitis  in  New  York  and  New 
England  in  1916.     [See  Am.  J.  P.  H.,  Feb.,  1917,  p.  117.] 

9.  What   proportion   of   children    "take"   the   common   children's 
diseases  at  some  time?     [See  Am.  J.  P.  H.,  Sept.,  1916,  p.  971.] 


APPENDIX  I 
REFERENCES 

To  study  demography,  or  even  vital  statistics,  seriously 
one  must  have  at  hand  several  of  the  standard  textbooks 
on  .the  statistical  method,  and  certain  of  the  more  recent 
federal,  state  and  municipal  reports.  One  must  also  have 
access  to  files  of  certain  periodicals.  The  following  is  a 
list  of  some  of  the  more  important  of  these  references.  It 
is  far  from  being  complete,  and  is  intended  merely  to  pave 
the  way  for  further  searches  in  the  library. 

A  complete  list  of  references  to  books  and  articles  on  the 
many  phases  of  the  subject  would  be  overwhelming.  The 
most  recent  writings  on  vital  statistics  are  not  necessarily 
the  best  for  the  beginner  to  study,  as  some  of  the  soundest 
and  most  logical  monographs  were  written  many  years  ago. 
Of  course,  the  most  recent  data  are  the  most  interesting  — 
but  that  is  another  matter. 

Many  references  to  particular  articles  will  be  found 
scattered  through  the  footnotes  of  this  book  and  printed  in 
connection  with  the  Exercises  and  Questions. 

GENERAL  TEXTBOOKS. 

NEWSHOLME,  ARTHUR.     Elements  of  Vital  Statistics.     Macmillan 
Co.,  1899. 

BOWLEY,  ARTHUR  L.     Elements  of  Statistics.     New  York,  Scribners, 
1907. 

BOWLEY,  ARTHUR  L.     An  Elementary  Manual  of  Statistics.     Lon- 
don, MacDonald  and  Evans,  1910. 

ELDERTON,  W.  PALIN  and  ETHEL  M.  ELDERTON.     Primer  of  Statis- 
tics.    New  York,  Macmillan  Co. 
459 


460  APPENDIX  I 

KING,  WELLFOBD  J.     The  Elements  of  Statistical  Method.     New 

York,  Macmillan  Co.,  1912. 
TRASK,   JOHN  W.     Vital  Statistics  —  a  report  published  by  the 

U.  S.  Public  Health  Service,  Apr.  3,  1914. 
YULE,  G.  UDNY.     Introduction  to  the  Theory  of  Statistics.     London, 

Griffin  &  Co.,  1912. 
WHIPPLE,  GEORGE  C.     Typhoid  Fever.     New  York,  John  Wiley  & 

Sons,  Inc.,1908. 
KOREN,  JOHN.    History  of  Statistics.     New  York,  Macmillan  Co., 

1918. 

PERIODICALS. 

AMERICAN  STATISTICAL  ASSOCIATION.    Quarterly  Publications.    -Vol. 

I  in  1888. 
AMERICAN  JOURNAL  OF  PUBLIC  HEALTH.     Monthly.     The  official 

publication  of  the  American  Public  Health  Association. 
PUBLIC  HEALTH  REPORTS.     Weekly.     Published  by  the  U.  S.  Public 

Health  Service. 

U.  S.  BUREAU  OF  LABOR  STATISTICS.     Monthly  Review. 
JOURNAL  OF  THE  ROYAL  STATISTICAL  SOCIETY. 

ANNUAL,  MONTHLY  AND  WEEKLY  REPORTS. 

There  are  scores  of  annual  reports  which  deal  with  vital 
statistics.     The  following  are  illustrative: 

U:  S.  BUREAU  OF  THE  CENSUS.  Mortality  Statistics.  Annually 
since  1900. 

ENGLAND  AND  WALES.  Annual  reports  of  Registrar-General.  (79th 
report  in  1916.) 

MASSACHUSETTS  STATE  REGISTRATION  REPORTS.  Annually  since 
1842. 

MASSACHUSETTS  STATE  BOARD  OF  HEALTH  (now  Department  of 
Health).  Annually  since  1870. 

STATE  DEPARTMENTS  OF  HEALTH  of  New  York,  New  Jersey,  Penn- 
sylvania, Ohio,  Michigan,  Maine,  New  Hampshire,  Connecticut, 
etc. 

ANNUAL  REPORTS  OF  BOARDS  OF  HEALTH  of  New  York  City,  Boston, 
Philadelphia,  Chicago,  Providence,  etc. 

Some  boards  of  health  publish  monthly  reports  —  New  York,  Massa- 
chusetts, Ohio,  etc. 

Some  city  health  departments  publish  weekly  reports  —  New  York, 
Chicago,  etc. 


APPENDIX  I  461 

DEMOGRAPHY. 

STATISTIQUE  GENERALE  DE  LA  FRANCE.  Statistique  Internationale 
du  Mouvement  de  la  Population  d'apres  les  registres  d'etat  civil, 
1907,  1913. 

WESTERGAARD,  HAROLD.  Die  Lehre  von  der  Mortalitat  und  Mor- 
bilitat,  anthropologisch-statistische  Untersuchungen.  Jena. 
Gustav  Fischer,  1901. 

GRAUNT,  CAPT.  JOHN.  Natural  and  Political  Observations  based 
upon  Bills  of  Mortality.  1662.  (Historical  value.) 

CHADWICK,  EDWIN.     Health  of  Nations.     (Historical  value.) 

FARR,  WILLIAM.  Vital  Statistics  —  a  memorial  volume  of  selec- 
tions from  his  reports  and  writings.  Edited  by  Noel  A.  Hum- 
phreys, London.  Office  of  the  Sanitary  Institute. 

MEITZEN,  DR.  AUGUST.  History  Theory  and  Technique  of  Statis- 
tics. Translated  by  Dr.  Roland  P.  Falkner.  Annals  of  the  Am. 
Acad.  of  Political  and  Social  Science,  1891. 

PEARSON,  KARL.  Life,  Letters  and  Labors  of  Sir  Francis  Galton, 
Vol.  I.  Cambridge,  England,  University  Press,  1914. 

BAILEY,  WM.  B.  Modern  Social  Conditions.  New  York,  Century 
Co.,  1906. 

ARITHMETIC. 

WEST,  CARL  S.  Introduction  to  Mathematical  Statistics.  Colum- 
bus, R.  G.  Adams  &  Co.,  1918. 

BAILEY,  W.  B.  and  JOSEPH  CUMMINGS.  Statistics.  Chicago,  A.  C. 
McClurg  Co.,  1917. 

WESTERGAARD,  HAROLD.  Scope  and  Methods  of  Statistics.  Quar. 
Pub.  Am.  Sta.  Asso.,  XV,  1916,  pp.  225-291. 

SECRIST,  HORACE.  Introduction  to  Statistical  Methods.  New 
York,  Macmillan  Co.,  1917. 

SAXELBY,  F.  M.  A  Course  in  Practical  Mathematics.  London, 
Longmans,  Green  &  Co.,  1908. 

THOMPSON,  SYLVANUS  P.  Calculus  Made  Easy.  London,  Mac- 
millan  Co.,  1917. 

GRAPHICS. 

REINHARDT,  CHAS.  W.  Lettering  for  Draftsmen,  Engineers  and 
Students.  New  York,  D.  Van  Nostrand  Co.,  1909. 

PEDDLE,  JOHN  B.  The  Construction  of  Graphical  Charts.  New 
York,  McGraw-Hill  Co.,  1910. 


462  APPENDIX  I 

BRINTON,  WILLARD  C.      Graphic  Methods  for  Presenting  Facts. 

New  York,  Engineering  Magazine  Co.,  1914. 
FISHER,  IRVING.     The  Ratio  Chart.     Quar.  Pub.  Am.  Sta.  Asso., 

1917,  p.  577. 

CENSUS  —  REGISTRATION. 

WILBUR,  CRESS Y  L.     The  Federal  Registration  Service  of  the  United 

States:  its  development,  problems  and  defects.     U.  S.  Bureau  of 

the  Census,  1916. 
NEWSHOLME,  ARTHUR.     A  National   System   of   Notification   and 

Registration.     Jour.  Royal.  Sta.  Soc.,  Vol.  59,  p.  1,  1896. 
DURAND,  E.  DANA.     Changes  in  Census  Methods  for  the  Census  of 

1910.     Am.  Jour,  of  Sociology,  1910. 
U.  S.  BUREAU  OF  THE  CENSUS.     American  Census  Taking  from  the 

First  Census  of  the  United  States,  1908. 
U.  S.  BUREAU  OF  THE  CENSUS.     Index  to  Occupations,  alphabetical 

and  classified,  1915. 


POPULATION. 

UNITED     STATES     CENSUS,     1790-1900.     Comprehensive     reports, 

usually  in  several  volumes,  published  every  ten  years. 
U.  S.  BUREAU  OF  THE  CENSUS.     1910.     Population,  Vols.  I,  II  and 

III. 
U.  S.  BUREAU  OF  THE  CENSUS.     Annual  Estimates  of  Population, 

are    published    in    a    series    of   bulletins.       Bulletin    133,    for 

1916. 
U.  S.  BUREAU  OF  THE  CENSUS.     A  Century  of  Population  Growth, 

1790-1900.     Pub.  in  1909. 
MASSACHUSETTS    STATE    CENSUS.     Intermediate    between    federal 

censuses  since  1845.     [Last  published  report  in  1905;  report  for 

1915  in  preparation.] 

LEROY-BEAULIEU,  P.    The  Influence  of  Civilization  on  the  Move- 
ment of  Population.     Jour.  Royal  Sta.  Soc.,  Vol.  54,  1891. 
FRANKLIN,   BENJAMIN.     Observations   concerning  the   Increase   of 

Mankind.     Book,  Philadelphia,  1751. 
JARVIS,  E.     History  of  the  Progress  of  Population  of  the  United 

States.     Book,  Boston,  1877. 
BAILEY,  W.  B.     Modern  Social  Conditions.     N.  Y.,  Century  Co., 

1906. 


APPENDIX  I  463 

GENERAL-RATES. 

NEWSHOLME,  A.     The  Declining  Birth-rate.     New  York,  Moffat, 

Yard  &  Co.,  1911. 
U.  S.  Bureau  of  the.  Census.     Birth  Statistics.    First  annual  report 

in  1915. 
HUMPHREYS,  N.  A.     Value  of  the  Death-rate  as  a  Test  of  Sanitary 

Conditions.     Jour.  Royal  Statistical  Society,  Vol.  37,  1874. 
YULE,  G.  M.    On  the  Changes  in  the  Marriage  and  Birth-rates  in 

England  and  Wales  during  the  past  Half  Century.    Jour.  Royal 

Sta.  Soc.,  Vol.  69,  p.  88,  1906. 

SPECIFIC  RATES. 

PEARSON,  KARL,  ALICE  LEE  and  ETHEL  M.  ELDERTON.  On  the 
Correction  of  Death-rates,  1910. 

GUILFOY,  WM.  H.  The  Death-rate  of  New  York  as  affected  by  the 
Cosmopolitan  Character  of  its  Population.  Quar.  Pub.  Am. 
Sta.  Asso.,  1907. 

ANDREW,  J.  GRANT.  Age  Incidence,  Sex  and  Comparative  Fre- 
quency in  Disease.  London,  Bailliere,  Tindall  &  Cox,  1909. 

CAUSES  OF  DEATH. 
A.  P.  H.  A.  COMMITTEE  REPORT.     The  Accuracy  of  Certified  Causes 

of  Death.     Public  Health  Reports,  Sept.  28,  1917,  pp.  1557-1632. 
U.  S.  BUREAU  OF  THE  CENSUS.     Manual  of  the  International  List 

of  Causes  of  Death,  1911. 

U.  S.  BUREAU  OF  THE  CENSUS.     Index  of  Joint  Causes  of  Death,  1914. 
U.  S.  BUREAU  OF  THE  CENSUS.     Physicians'  Pocket  Reference  to  the 

International  List  of  Causes  of  Death,  1918. 

PROBABILITY. 

DAVENPORT,  CHAS.  B.     Statistical  Methods,  with  Special  Reference 

to  Biological  Variations.     Second  edition,  New  York,  John  Wiley 

and  Sons,  Inc.,  1904. 
FISHER,  ARNE.    The  Mathematical  Theory  of  Probabilities.     New 

York,  Macmillan  Co.,  1915. 
WHIPPLE,  GEORGE  C.    The  Element  of  Chance  in  Sanitation.    Jour. 

Franklin  Institute,  July  and  Aug.,  1916. 
WELD,  LEROY  D.     Theory  of  Errors  and  Least  Squares.     New  York, 

Macmillan  Co.,  1916. 


464  APPENDIX  I 

GOODWIN,  A.  M.  Elements  of  the  Precision  of  Measurements  and 
Graphical  Methods.  New  York,  McGraw-Hill  Co.,  1913. 

LA  PLACE,  P.  S.,  MARQUIS  DE.  ThSorie  analytique  des  probability's, ! 
1814.  (Historical  value.) 

QUETELET,  L.  A.  S.  Lettres  sur  la  theorie  des  probabilites,  appli-l 
quee  aux  sciences  morales  et  politiques,  1846.  (English  trans-- 
lation  by  O.  G.  Downs,  1849.) 

BROWNLEE,  JOHN.  The  Mathematical  Theory  of  Random  Migra- 
tion and  Epidemic  Distribution.  Proc.  Royal  Soc.  of  Edin- 
burgh, Vol.  31,  p.  262,  1910-11. 

CORRELATION. 

JEVONS,  W.  STANLEY.     The  Principles  of  Science.     London,  Mac- 

millan  Co.,  1907. 
PEARSON,  KARL,  ALICE  LEE  and  ETHEL  M.  ELDERTON.    On  the 

Correlation  of  Death-rates.     Jour.  Royal  Sta.  Soc.,  Vol.  73, 

p.  534,  1910. 

LIFE  TABLES. 

MOIR,  HENRY.    Life  Assurance  Primer.     New  York,  The  Spectator 

.  Co.,  1912. 
HENDERSON,  ROBERT.     Mortality  Laws  and  Statistics.     New  York, 

John  Wiley  &  Sons,  Inc.,  1915. 
GLOVER,  JAS.  W.    United  States  Life  Tables,  1910.    U.  S.  Census, 

1916. 
BURN,  JOSEPH.    Vital  Statistics  Explained.    London.  Constable  and 

Company,  Ltd.,  1914. 


APPENDIX  II 

THE  MODEL  STATE  LAW  FOR  MORBIDITY  REPORTS 

ADOPTED  BY  THE  ELEVENTH  ANNUAL  CONFERENCE  OF  STATE  AND  TERRI- 
TORIAL HEALTH  AUTHORITIES  WITH  THE  UNITED  STATES  PUBLIC 
HEALTH  SERVICE,  MINNEAPOLIS,  JUNE  16,  1913. 

A  Bill  To  provide  for  the  notification  of  the  occurrence  and  prevalence  of  certain  diseacer. 

Be  it  enacted  by  the  Senate  and  General  Assembly  of  the  State  of : 

SECTION  1.  It  shall  be,  and  is  hereby,  made  the  duty  of  the  State 
department  of  health  (or  commissioner  or  board  of  health)  to  keep 
currently  informed  of  the  occurrence,  geographic  distribution,  and 
prevalence  of  the  preventable  diseases  throughout  the  State,  and  for 
this  purpose  there  shall  be  established  in  the  State  department  of  health 
a  bureau  (or  division)  of  sanitary  reports  which  shall,  under  the  direc- 
tion of  the  State  commissioner  of  health  (State  health  officer  or  secre- 
tary of  the  State  board  of  health),  be  in  charge  of  an  assistant  com- 
missioner of  health  who  shall  receive  an  annual  salary  of dollars 

and  the  necessary  expenses  incurred  in  the  performance  of  his  duties. 
The  State  department  of  health  shall  provide  such  clerical  and  other 
assistance  as  may  be  necessary  for  the  establishment  and  maintenance 
of  said  bureau. 

SEC.  2.  The  following-named  diseases  and  disabilities  are  hereby 
made  notifiable  and  the  occurrence  of  cases  shall  be  reported  as  herein 
provided:  » 

GROUP  I.  —  INFECTIOUS  DISEASES 

Actinomycosis.  Dengue. 

Anthrax.  Diphtheria. 

Chicken-pox.  Dysentery:. 
Cholera.     Asiatic  (also  cholera  nos-          (a)   Amebic. 

tras  when  Asiatic  cholera  is  pres-  (6)   Bacillary. 

ent  or  its  importation  threatened).  Favus. 

Continued  fever  lasting  seven  days.  German  measles. 

465 


466 


APPENDIX   II 


GROUP   I.  —  INFECTIOUS    DIS- 
EASES —  Continued 

Glanders. 

Hookworm  disease. 

Leprosy. 

Malaria. 

Measles. 

Meningitis: 

(a)   Epidemic  cerebrospinal. 
(6)   Tuberculous. 

Mumps. 

Ophthalmia  neonatorum   (conjunc- 
tivitis of  new  born  infants). 

Paragonimiasis  (endemic  hemoptysis) . 

Paratyphoid  fever. 

Plague. 

Pneumonia. 

Poliomyelitis  (acute  infectious). 

Rabies. 

Rocky  Mountain  spotted,   or  tick, 
fever. 

Scarlet  fever. 

Septic  sore  throat. 

Smallpox. 

Tetanus. 

Trachoma. 


Typhus  fever. 
Whooping  cough. 
Yellow  fever. 


GROUP     II.  —  OCCUPATIONAL      DIS- 
EASES  AND    INJURIES. 

Arsenic  poisoning. 
Brass  poisoning. 
Carbon  monoxide  poisoning. 
Lead  poisoning. 
Mercury  poisoning. 
Natural  gas  poisoning. 
Phosphorous  poisoning. 
Wood  alcohol  poisoning. 
Naphtha  poisoning. 
Bisulphide  of  carbon  poisoning. 
Dinitrobenzine  poisoning. 
Caisson  disease  (compressed-air 

illness). 
Any  other  disease  or  disability 

contracted  as  a  result  of  the 

nature  of  the  person's  employ^ 

ment. 

GROUP   III.  —  VENEREAL  DISEASES 

Gonococcus  infection. 
Syphilis. 


Trichinosis. 

Tuberculosis  (all  forms,  the  organ  or  GROUP  iv.  —  DISEASES  OF  UN- 

part  affected  in  each  case  to  be  KNOWN  ORIGIN. 

specified) .  Pellagra . 

Typhoid  fever.  Cancer. 

Provided,  That  the  State  department  of  health  (or  board  of  health) 
may  from  time  to  time,  in  its  discretion,  declare  additional  diseases 
notifiable  and  subject  to  the  provisions  of  this  act. 

SEC.  3.   Each  and  every  physician  practicing  in  the  State  of  - 
who  treats  or  examines  any  person  suffering  from  or  afflicted  with,  or 
suspected  to  be  suffering  from  or  afflicted  with,  any  one  of  the  notifiable 
diseases  shall  immediately  report  such  case  of  notifiable  disease  in  writ- 
ing to  the  local  health  authority  having  jurisdiction.    Said  report  shall 


APPENDIX  II  467 

»  forwarded  either  by  mail  or  by  special  messenger  and  shall  give  the 
•flowing  information: 

1.  The  date  when  the  report  is  made. 
.     2.  The  name  of  the  disease  or  suspected  disease. 

3.  The  name,  age,  sex,  color,  occupation,  address,  and  school  attended 
r  place  of  employment  of  patient. 

4.  Number  of  adults  and  children  in  the  household. 

5.  Source  or  probable  source  of  infection  or  the  origin  or  probable 
rigin  of  the  disease. 

6.  Name  and  address  of  the  reporting  physician. 

Provided,  That  if  the  disease  is,  or  is  suspected  to  be,  smallpox  the 

3port  shall,  in  addition,  show  whether  the  disease  is  of  the  mild  or 

indent   type  and  whether  the  patient  has  ever  been  successively 

accinated,  and,  if  the  patient  has  been  successfully  vaccinated,  the 

umber  of  times  and  dates  or  approximate  dates  of  such  vaccination; 

nd  if  the  disease  is,  or  is  suspected  to  be,  cholera,  diphtheria,  plague, 

carlet  fever,  smallpox,  or  yellow  fever,  the  physician  shall,  in  addition 

o  the  written  report,  give  immediate  notice  of  the  case  to  the  local 

,  ealth  authority  in  the  most  expeditious  manner  available;  and  if  the 

i  Lisease  is,  or  is  suspected  to  be,  typhoid  fever,  scarlet  fever,  diphtheria 

I  >r  septic  sore  throat  the  report  shall  also  show  whether  the  patient  has 

'  >een,  or  any  member  of  the  household  in  which  the  patient  resides  is, 

ngaged  or  employed  in  the  handling  of  milk  for  sale  or  preliminary  to 

j  ale:  And  provided  further,  That  in  the  reports  of  cases  of  the  venereal 

!  liseases  the  name  and  address  of  the  patient  need  not  be  given. 

(    SEC.  4.   The  requirements  of  the  preceding  section  shall  be  applicable 

o  physicians  attending  patients  ill  with  any  of  the  notifiable  diseases 

Q  hospitals,  asylums,  or  other  institutions,  public  or  private:  Provided, 

Chat  the  superintendent  or  other  person  in  charge  of  any  such  hospital, 

,sylum,  or  other  institution  in  which  the  sick  are  cared  for  may,  with 

he  written  consent  of  the  local  health  officer  (or  board  of  health)  having 

urisdiction,  report  in  the  place  of  the  attending  physician  or  physicians 

-he  cases  of  notifiable  diseases  and  disabilities  occurring  in  or  admitted 

;o  said  hospital,  asylum,  or  other  institution  in  the  same  manner  as  that 

prescribed  by  physicians. 

SEC.  5.  Whenever  a  person  is  known,  or  is  suspected,  to  be  afflicted 
with  a  notifiable  disease,  or  whenever  the  eyes  of  an  infant  under  two 
weeks  of  age  become  reddened,  inflamed,  or  swollen,  or  contain  an 
unnatural  discharge,  and  no  physician  is  in  attendance,  an  immediate 
report  of  the  existence  of  the  case  shall  be  made  to  the  local  health  officer 


468  .  APPENDIX  II 

by  the  midwife,  nurse,  attendant,  or  other  person  in  charge  of  the 
patient. 

SEC.  6.  Teachers  or  other  persons  employed  in,  or  in  charge  of,  public 
or  private  schools,  including  Sunday  Schools,  shall  report  immediately 
to  the  local  health  officer  each  and  every  known  or  suspected  case  of  a 
notifiable  disease  in  persons  attending  or  employed  in  their  respective 
schools. 

SEC.  7.  The  written  reports  of  cases  of  the  notifiable  disease  required 
by  this  act  of  physicians  shall  be  made  upon  blanks  supplied  for  the 
purpose,  through  the  local  health  authorities,  by  the  State  department 
of  health.  These  blanks  shall  conform  to  that  adopted  and  approved 
by  the  State  and  Territorial  health  authorities  in  conference  with  the 
United  States  Public  Health  Service. 

SEC.  8.  Local  health  officers  or  boards  of  health  shall  within  seven 
days  after  the  receipt  by  them  of  reports  of  cases  of  the  notifiable 
diseases  forward  by  mail  to  the  State  department  of  health  the  original 
written  reports  made  by  physicians,  after  first  having  transcribed  the 
information  given  in  the  respective  reports  in  a  book  or  other  form  of 
record  for  the  permanent  files  of  the  local  health  office.  On  each  report 
thus  forwarded  the  local  health  officer  shall  state  whether  the  case  to 
which  the  report  pertains  was  visited  or  otherwise  investigated  by  a 
representative  of  the  local  health  office  and  whether  measures  were 
taken  to  prevent  the  spread  of  the  disease  or  the  occurrence  of  addi- 
tional cases. 

SEC.  9.  Local  health  officers  or  boards  of  health  shall,  in  addition  to 
the  provisions  of  section  8,  report  to  the  State  department  of  health  in 
such  manner  and  at  such  times  as  the  State  department  of  health  may 
require  by  regulation  the  number  of  new  cases  of  each  of  -the  notifiable 
diseases  reported  to  said  local  health  officers  or  boards  of  health. 

SEC.  10.  Whenever  there  occurs  within  the  jurisdiction  of  a  local 
health  officer  or  board  of  health  an  epidemic  of  a  notifiable  disease,  the 
local  health  officer  or  board  of  health  shall,  within  30  days  after  the 
epidemic  shall  have  subsided,  make  a  report  to  the  State  department  of 
health  of  the  number  of  cases  occurring  in  the  epidemic,  the  number  of 
cases  terminating  fatally,  the  origin  of  the  epidemic,  and  the  means  by 
which  the  disease  was  spread:  Provided,  That  whenever  the  State 
department  of  health  has  taken  charge  of  the  control  and  suppression  or 
undertaken  the  investigation  of  the  epidemic,  the  local  health  authority 
having  jurisdiction  need  not  make  the  report  otherwise  required. 

SEC.  11.   No  person  shall  be  appointed  to  the  position  of  local  health 


APPENDIX  II  469 

officer  in  any  city,  town,  or  county  until  after  the  qualifications  of  said 
person  have  been  approved  by  the  State  department  of  health. 

SEC.  12.  In  localities  in  which  there  are  no  local  health  officers  or 
boards  of  health,  and  in  localities  in  which,  although  there  are  health 
officers  or  boards  of  health,  adequate  provision  has  not,  in  the  opinion 
of  the  State  department  of  health,  been  made  for  the  proper  notification, 
investigation,  and  control  of  notifiable  disease,  and  in  localities  in  which 
the  local  health  authorities  fail  to  carry  out  the  provisions  of  this  act, 
the  State  department  of  health  shall  appoint  properly  qualified  sanitary 
officers  to  act  as  local  health  officers  and  to  prevent  the  spread  of  disease 
in  and  from  such  localities  and  to  enforce  the  provisions  of  this  act: 
Provided,  That  salaries  and  other  expenses  incurred  under  the  provisions 
of  this  section  shall  be  paid  by  the  local  authorities. 

SEC.  13.  Any  physician  or  other  person  or  persons  who  shall  fail, 
neglect  or  refuse  to  comply  with,  or  who  shall  violate  any  of  the  pro- 
visions of  this  act  shall  be  guilty  of  a  misdemeanor,  and  upon  conviction 

thereof  shall  be  sentenced  to  pay  a  fine  of  not  less  than dollars 

nor  more  than  —  —  dollars  or  to  imprisonment  for  not  less  than 

days  nor  more  than days  for  each  offense:  Provided,  That  in  the 

case  of  a  physician  his  license  to  practice  medicine  within  the  State  may 
be  revoked  in  accordance  with  existing  statutory  provisions. 

SEC.  14.  No  license  to  practice  medicine  shall  be  issued  to  any  person 
until  after  the  applicant  shall  have  filed  with  the  State  licensing  board 
a  statement,  signed  and  sworn  to  before  a  notary  or  other  officer  quali- 
fied to  administer  oaths,  that  said  applicant  has  familiarized  himself 
with  the  requirements  of  this  act,  a  copy  of  which  sworn  statement  shall 
be  forwarded  to  the  State  department  of  health. 

SEC.  15.  Each  and  every  person  engaged  in  the  practice  of  medicine 
shall  display  in  a  prominent  place  in  his  or  her  office  a  card  upon  which 
sections  2,  3,  4,  7,  13,  14,  and  15  of  this  act  have  been  printed  with  type 
not  smaller  than  10-point.  A  similar  card  shall  be  displayed  in  a  prom- 
inent place  in  the  office  of  each  and  every  hospital,  asylum,  or  other 
public  or  private  institution  for  the  treatment  of  the  sick.  These  cards 
shall  each  be  not  less  than  1  square  foot  in  size  and  shall  be  furnished 
to  institutions  and  licensed  physicians  without  cost  by  the  State  de- 
partment of  health. 

SEC.  16.  The  sum  of  —  —  dollars  is  hereby  appropriated  from  any 
money  in  the  State  treasury  not  otherwise  appropriated  for  carrying 
out  the  provisions  of  this  act. 

SEC.  17.  This  act  shall  take  effect  immediately,  and  all  acts  or  parts 
of  acts  inconsistent  with  the  provisions  of  this  act  are  hereby  repealed. 


470 


APPENDIX  II 


THE  STANDARD   MORBIDITY  NOTIFICATION  BLANK 

The  following  model  notification  blank  was  also  adopted  by  the  conference  of  state  and 
territorial  health  authorities  with  the  United  States  Public  Health  Service,  June  16, 1913, 
as  the  standard  notification  blank  referred  to  in  section  7  of  the  Model  Law  as  the  one  lo 
be  used  in  the  reporting  of  cases  of  the  notifiable  diseases.  This  blank  is  intended  to  be 
printed  on  a  post  card: 

[Face  of  card.) 

.,191.. 


(Date.) 

Disease  or  suspected  disease 

Patient's  name ,  age ,  sex ,  color 

Patient's  address ,  occupation 

School  attended  or  place  of  employment 

Number  in  household:  Adults children 

Probable  source  of  infection  or  origin  of  disease 

If  disease  is  smallpox,  type ,  number  of  times 

successfully  vaccinated  and  approximate  dates 

If  typhoid  fever,  scarlet  fever,  diphtheria,  or  septic  sore  throat,  was  patient,  or  is  any 

member  of  household  engaged  in  the  production  of  handling  of  milk 

Address  of  reporting  physician 

Signature  of  physician    


[Reverse  of  card.] 


For  use  of  local  health  department. 


II 


Health  Department, 

(City) 

(State) 


APPENDIX  II  471 

HOSPITAL  DISCHARGE   CERTIFICATE 

Suggested  by  Bolduan  for  use  in  connection  with  hospital  morbidity  reports. 
DISCHARGE  CERTIFICATE. 


Name  of  hospital Hospital  admission  No. . 

Sex Age 

How  admitted  —  Ambulance 


or  White.  Hebrew, 

own  application  Colored.  Gentile. 

or  Mongolian. 
(Tabulation            transfer  from 


No.)  other  hospital.  Place  of  birth 


Patient's  address Single  or  married  or  widowed  or  divorced  or 

Borough unknown. 

Date  admitted Discharged  to  — 

Date  discharged Home. 

Days  in  hospital months Other  hospital. 

days Convalescent  retreat. 

(If  over  a  year,  omit  the  days  and  give  only  Coroner. 

years  and  months.) 
Occupation  —  (a)  Trade,  profession,  or  particular  kind  of  work. 

(6)  General  nature  of  the  industry,  business,  or  establishment  in  which 
employed  (or  employer). 

Diagnosis 

and 

Complications 

If  operated  upon,  state  nature  of  operation 

Condition  on  discharge:  Cured.    Improved.    Unimproved. 

Died  — Autopsy. 

No  autopsy. 

Signed 

House  Physician  —  Surgeon. 


APPENDIX  III 

THE  MODEL  STATE  LAW  FOR  THE  REGISTRATION   OF 
BIRTHS  AND  DEATHS 

A-  Bill 1  To  provide  for  the  registration  of  all  births  and  deaths  in  the  State  of . 

NOTE.  —After  the  bill  has  been  prepared  for  presentation  to  the  legislature  of  a  State, 
the  title  should  be  carefully  revised  by  competent  legal  authority. 

Be  it  enacted  by  the  legislature  of  the  Stat-e  of 

SECTION  1.  That  the  State  board  of  health  shall  have  charge  of  the 
registration  of  births  and  deaths;  shall  prepare  the  necessary  instruc- 
tions, forms,  and  blanks  for  obtaining  and  preserving  such  records  and 
shall  procure  the  faithful  registration  of  the  same  in  each  primary  regis- 
tration district  as  constituted  in  section  3  of  this  act,  and  in  the  central 
bureau  of  vital  statistics  at  the  capital  of  the  State.  The  said  board 
shall  be  charged  with  the  uniform  and  thorough  enforcement  of  the  law 
throughout  the  State,  and  shall  from  time  to  time  recommend  any 
additional  legislation2  that  may  be  necessary  for  this  purpose.. 

SEC.  2.  That  the  secretary  of  the  State  board  of  health  shall  have 
general  supervision  over  the  central  bureau  of  vital  statistics,  which  is 
hereby  authorized  to  be  established  by  said  board,  and  which  shall  be 
under  the  immediate  direction  of  the  State  registrar  of  vital  statistics, 
whom  the  State  board  of  health  shall  appoint  within  thirty  days  after 
the  taking  effect  of  this  law,  and  who  shall  be  a  medical  practitioner  of 
not  less  than  five  years'  practice  in  his  profession,  and  a  competent  vital 
statistician.  The  State  registrar  of  vital  statistics  shall  hold  office  for 
four  years  and  until  his  successor  has  been  appointed  and  has  qualified, 
unless  such  office  shall  sooner  become  vacant  by  death,  disqualification, 

1  Before  introducing  this  bill  in  any  legislature  it  should  be  carefully 
redrafted  by  a  competent  lawyer  and  submitted  to  the  Bureau  of  the 
Census  for  criticism. 

2  The  words  "and  shall  promulgate  any  additional  rules  or  regula- 
tions" may  be  inserted  in  bills  prepared  for  States  in  which  the  State 
board  of  health  has  power  to  make  rules  and  regulations  having  the 
effect  of  law. 

472 


APPENDIX  III  473 

operation  of  law,  or  other  causes.  Any  vacancy  occurring  in  such 
office  shall  be  filled  for  the  unexpired  term  by  the  State  board  of  health. 
At  least  ten  days  before  the  expiration  of  the  term  of  office  of  the  State 
registrar  of  vital  statistics,  his  successor  shall  be  appointed  by  the  State 
board  of  health.  The  State  registrar  of  vital  statistics  shall  receive  an 

annual  salary  at  the  rate  of dollars  from  the  date  of  his  entering 

upon  the  discharge  of  the  duties  of  his  office.  The  State  board  of  health 
shall  provide  for  such  clerical  and  other  assistants  as  may  be  necessary 
for  the  purposes  of  this  act,  who  shall  serve  during  the  pleasure  of  tho 
board,  and  shall  fix  the  compensation  of  persons  thus  employed  within 
the  amount  appropriated  therefor  by  the  legislature.  The  -custodian 
of  the  capitol  shall  provide  for  the  bureau  of  vital  statistics  in  the  State 

capitol  at suitable  offices,  which  shall  be  properly  equipped  with 

fireproof  vault  and  filing  cases  for  the  permanent  and  safe  preservation 
of  all  official  records,  made  and  returned  under  this  act. 

SEC.  3.  That  for  the  purposes  of  this  act  the  State  shall  be  divided 
into  registration  districts  as  follows:  Each  city,  each  incorporated 
town,  and  each  township l  shall  constitute  a  primary  registration  dis- 
trict :  Provided,  That  the  State  board  of  health  may  combine  two  or  more 
primary  registration  districts  when  necessary  to  facilitate  registration. 

SEC.  4.  That  within  ninety  days  after  the  taking  effect  of  this  act,  or 
as  soon  thereafter  as  possible,  the  State  board  of  health  shall  appoint 
a  local  registrar  of  vital  statistics  for  each  registration  district  in  the 
State.2  The  term  of  office  of  each  local  registrar  so  appointed  shall  be 

1  Or  other  primary  political   unit,  as  "town,"  "precinct,"  "civil 
district,"  "hundred,"  etc.     When  there  are  no  such  units  available,  the 
following  substitutes  for  section  3  may  be  employed:  Section  3.     That 
for  the  purposes  of  this  act  the  State  shall  be  divided  into  registration 
districts  as  follows:   Each  city  and  each  incorporated  town  shall  con- 
stitute a  primary  registration  district;    and  for  that  portion  of  each 
county  outside  of  the  cities  and  incorporated  towns  therein  the  State 
board  of  health  shall  define  and  designate  the  boundaries  of  a  sufficient 
number  of  rural  registration  districts,  which  districts  it  may  change  or 
combine  from  time  to  time  as  may  be  necessary  to  insure  the  convenience 
and  completeness  of  registration. 

2  This  method  of  appointment  of  local  registrars  by  the  State  board 
of  health  —  or  perhaps  by  the  State  registrar  or  upon  his  nomination  — 
with  a  reasonably  long  term  of  service  and  subject  to  removal  for  neglect 
of  duty,  is  the  preferable  one  for  efficient  service.     Should  there  be 
objection,  however,  to  the  creation  of  new  offices,  the  section  may  be 
redrafted  so  that  it  will  provide  that  township,  village,  or  city  clerks,  or 
other  suitable  officials,  shall  be  the  local  registrars. 


474  APPENDIX  III 

four  years,  and  until  his  successor  has  been  appointed  and  has  qualified, 
unless  such  office  shall  sooner  become  vacant  by  death,  disqualification, 
operation  of  law,  or  other  causes:  Provided,  That  in  cities  where  health 
officers  or  other  officials  are,  in  the  judgment  of  the  State  board  of 
health,  conducting  effective  registration  of  births  and  deaths  under 
local  ordinances  at  the  time  of  the  taking  effect  of  this  act  such  officials 
may  be  appointed  as  registrars  in  and  for  such  cities,  and  shall  be 
subject  to  the  rules  and  regulations  of  the  State  registrar  and  to  all  of 
the  provisions  of  this  act.  Any  vacancy  occurring  in  the  office  of  local 
registrar  of  vital  statistics  shall  be  filled  for  the  unexpired  term  by  the 
State  board  of  health.  At  least  ten  days  before  the  expiration  of  the 
term  of  office  of  any  such  local  registrar  his  successor  shall  be  appointed 
by  the  State  board  of  health. 

Any  local  registrar  who,  in  the  judgment  of  the  State  board  of  health, 
fails  or  neglects  to  discharge  efficiently  the  duties  of  his  office  as  set  forth 
in  this  act,  or  to  make  prompt  and  complete  returns  of  births  and  deaths 
as  required  thereby,  shall  be  forthwith  removed  by  the  State  board  of 
health,  and  such  other  penalties  may  be  imposed  as  are  provided  under 
section  22  of  this  act. 

Each  local  registrar  shall,  immediately  upon  his  acceptance  of  ap- 
pointment as  such,  appoint  a  deputy,  whose  duty  it  shall  be  to  act  in 
his  stead  in  case  of  his  absence  or  disability;  and  such  deputy  shall  in 
writing  accept  such  appointment  and  be  subject  to  all  rules  and  regula- 
tions governing  local  registrars.  And  when  it  appears  necessary  for  the 
convenience  of  the  people  in  any  rural  district  the  local  registrar  is 
hereby  authorized,  with  the  approval  of  the  State  registrar,  to  appoint 
one  or  more  suitable  persons  to  act  as  subregistrars,  who  shall  be  author- 
ized to  receive  certificates  and  to  issue  burial  or  removal  permits  in  and 
for  such  portions  of  the  district  as  may  be  designated;  and  each  sub- 
registrar  shall  note  on  each  certificate,  over  his  signature,  the  date  of 
filing,  and  shall  forward  all  certificates  to  the  local  registrar  of  the 
district  within  ten  days,  and  in  all  cases  before  the  third  day  of  the 
following  month:  Provided,  That  each  subregistrar  shall  be  subject  to 
the  supervision  and  control  of  tne  State  registrar  and  may  be  by  him 
removed  for  neglect  or  failure  to  perform  his  duty  in  accordance  with  the 
provisions  of  this  act  or  the  rules  and  regulations  of  the  State  registrar, 
and  shall  be  subject  to  the  same  penalties  for  neglect  of  duty  as  the  local 
registrar. 

SEC.  5.  That  the  body  of  any  person  whose  death  occurs  in  this 
State,  or  which  shall  be  found  dead  therein,  shall  not  be  interred,  de- 
posited in  a  vault  or  tomb,  cremated  or  otherwise  disposed  of,  or  re- 


APPENDIX  III  475 

moved  from  or  into  any  registration  district,  or  be  temporarily  held 
pending  further  disposition  more  than  seventy-two  hours  after  death, 
unless  a  permit  for  burial,  removal,  or  other  disposition  thereof  shall 
have  been  properly  issued  by  the  local  registrar  of  the  registration 
district  in  which  the  death  occurred  or  the  body  was  found.1  And  no 
such  burial  or  removal  permit  shall  be  issued  by  any  registrar  until, 
wherever  practicable,  a  complete  and  satisfactory  certificate  of  death 
has  been  filed  with  him  as  hereinafter  provided:  Provided,  That  when 
a  dead  body  is  transported  from  outside  the  State  into  a  registration 

district  in for  burial,  the  transit  or  removal  permit,  issued  in 

accordance  with  the  law  and  health  regulations  of  the  place  where  the 
death  occurred,  shall  be  accepted  by  the  local  registrar  of  the  district 
into  which  the  body  has  been  transported  for  burial  or  other  disposition, 
as  a  basis  upon  which  he  may  issue  a  local  burial  permit;  he  shall  note 
upon  the  face  of  the  burial  permit  the  fact  that  it  was  a  body  shipped  in 
for  interment,  and  give  the  actual  place  of  death;  and  no  local  registrar 
shall  receive  any  fee  for  the  issuance  of  burial  or  removal  permits  under 
this  act  other  than  the  compensation  provided  in  section  20. 

SEC.  6.  That  a  stillborn  child  shall  be  registered  xas  a  birth  and  also 
as  a  death,  and  separate  certificates  of  both  the  birth  and  the  death 
shall  be  filed  with  the  local  registrar,  in  the  usual  form  and  manner,  the 
certificate  of  birth  to  contain  in  place  of  the  name  of  the  child,  the  word 
"stillbirth":  Provided,  That  a  certificate  of  birth  and  a  certificate  of 
death  shall  not  be  required  for  a  child  that  has  not  advanced  to  the  fifth 
month  of  uterogestation.  The  medical  certificate  of  the  cause  of  death 
shall  be  signed  by  the  attending  physician,  if  any,  and  shall  state  the 
cause  of  death  as  "stillborn,"  with  the  cause  of  the  stillbirth,  if  known, 
whether  a  premature  birth,  and,  if  born  prematurely,  the  period  of 
uterogestation,  in  months,  if  known;  and  a  burial  or  removal  permit 
of  the  prescribed  form  shall  be  required.  Midwives  shall  not  sign 
certificates  of  death  for  stillborn  children;  but  such  cases,  and  still- ^ 
births  occurring  without  attendance  of  either  physician  or  midwife, 
shall  be  treated  as  deaths  without  medical  attendance,  as  provided  for 
in  section  8  of  this  act. 

SEC.  7.  That  the  certificate  of  death  shall  contain  the  following 
items,  which  are  hereby  declared  necessary  for  the  legal,  social,  and 
sanitary  purposes  subserved  by  registration  records:2 

1  A  special  proviso  may  be  required  for  sparsely  settled  portions  of 
a  State. 

2  The  following  items  are  those  of  the  United  States  standard  certi- 
ficate of  death,  approved  by  the  Bureau  of  the  Census. 


476  APPENDIX  III 

(1)  Place  of  death,  including  State,  county,  township,  village,  or 
city.     If  in  a  city,  the  ward,  street,  and  house  number;  if  in  a  hospital 
or  other  institution,  the  name  of  the  same  to  be  given  instead  of  the 
street  and  house  number.     If  in  an  industrial  camp,  the  name  of  the 
camp  to  be  given. 

(2)  Full  name  of  decedent.     If  an  unnamed  child,  the  surname 
preceded  by  "Unnamed." 

(3)  Sex/ 

(4)  Color  or  race,  as  white,  black,  mulatto  (or  other  negro  descent), 
Indian,  Chinese,  Japanese,  or  other. 

(5)  Conjugal  condition,  as  single,  married,  widowed,  or  divorced. 

(6)  Date  of  birth,  including  the  year,  month,  and  day. 

(7)  Age,  in  years,  months,  and  days.     If  less  than  one  day,  the  hours 
or  minutes. 

(8)  Occupation'.     The  occupation  to  be  reported  of  any  person, 
male  or  female,  who  had  any  remunerative  employment,  with  the  state- 
ment of  (a)  trade,  profession  or  particular  kind  of  work;    (6)  general 
nature  of  industry,  business,  or  establishment  in  which  employed  (or 
employer). 

(9)   Birthplace;  at  least  State  or  foreign  country,  if  known. 

(10)  Name  of  father. 

(11)  Birthplace  of  father;  at  least  State  or  foreign  country,  if  known. 

(12)  Maiden  name  of  mother. 

(13)  Birthplace  of  mother;  at  least  State  or  foreign  country,  if  known. 

(14)  Signature  and  address  of  informant. 

(15)  Official  signature  of  registrar,  with  the  date  when  certificate 
was  filed,  and  registered  number. 

(16)  Date  of  death,  year,  month,  and  day. 

(17)  Certification  as  to  medical  attendance  on  decedent,  fact  and 
time  of  death,  time  last  seen  alive,  and  the  cause  of  death,  with  con- 
tributory (secondary)  cause  of  complication,  if  any,  and  duration  of 
each,  and  whether  attributed  to  dangerous  or  insanitary  conditions  of 
employment;  signature  and  address  of  physician  or  official  making  the 
medical  certificate. 

(18)  Length  of  residence  (for  inmates  of  hospitals  and  other  institu- 
tions; transients  or  recent  residents)  at  place  of  death  and  in  the  State, 
together  with  the  place  where  disease  was  contracted,  if  not  at  place  of 
death,  and  former  or  usual  residence. 

(19)  Place  of  burial  or  removal;  date  of  burial. 

(20)  Signature  and  address  of  undertaker  or  person  acting  as  such. 


APPENDIX  III  477 

The  personal  and  statistical  particulars  (items  1  to  13)  shall  be  authen- 
ticated by  the  signature  of  the  informant,  who  may  be  any  competent 
person  acquainted  with  the  facts. 

The  statement  of  facts  relating  to  the  disposition  of  the  body  shall 
be  signed  by  the  undertaker  or  person  acting  as  such. 

The  njedical  certificate  shall  be  made  and  signed  by  the  physician,  if 
any,  last  in  attendance  on  the  deceased,  who  shall  specify  the  time  in 
attendance,  the  time  he  last  saw  the  deceased  alive,  and  the  hour  of  the 
day  at  which  death  occurred.  And  he  shall  further  state  the  cause  of 
death,  so  as  to  show  the  course  of  disease  or  sequence  of  causes  resulting 
in  the  death,  giving  first  the  name  of  the  disease  causing  death  (primary 
cause),  and  the  contributory  (secondary)  cause,  if  any,  and  the  duration 
of  each.  Indefinite  and  unsatisfactory  terms,  denoting  only  symptoms 
of  disease  or  conditions  resulting  from  disease,  will  not  be  held  sufficient 
for  the  issuance  of  a  burial  or  removal  permit;  and  any  certificate  con- 
taining only  such  terms  as  defined  by  the  State  Registrar  shall  be 
returned  to  the  physician  or  person  making  the  medical  certificate  for 
correction  and  more  definite  statement.  Causes  of  death  which  may  be 
the  result  of  either  disease  or  violence  shall  be  carefully  defined;  and  if 
from  violence,  the  means  of  injury  shall  be  stated  and  whether  (prob- 
ably) accidental,  suicidal,  or  homicidal.1  And  for  deaths  in  hospitals, 
institutions,  or  of  nonresidents  the  physician  shall  supply  the  informa- 
tion required  under  this  head  (item  18),  if  he  is  able  to  do  so,  and  may 
state  where,  in  his  opinion,  the  disease  was  contracted. 

SEC.  8.  That  in  case  of  any  death  occurring  without  medical  attend- 
ance it  shall  be  the  duty  of  the  undertaker  to  notify  the  local  registrar 
of  such  death,  and  when  so  notified  the  registrar  shall,  prior  to  the 
issuance  of  the  permit,  inform  the  local  health  officer  and  refer  the  case 
to  him  for  immediate  investigation  and  certification:  Provided,  That 
when  the  local  health  officer  is  not  a  physician,  or  when  there  is  no  such 
official,  and  in  such  cases  only,  the  registrar  is  authorized  to  make  the 
certificate  and  return  from  the  statement  of  relatives  or  other  persons 
having  adequate  knowledge  of  the  facts :  Provided  further,  That  if  the 
registrar  has  reason  to  believe  that  the  death  may  have  been  due  to 
unlawful  act  or  neglect  he  shall  then  refer  the  case  to  the  coroner  or 
other  proper  officer  for  his  investigation  and  certification.  And  the 
coroner  or  other  proper  officer  whose  duty  it  is  to  hold  an  inquest  on  the 

1  In  some  States  the  question  whether  a  death  was  accidental,  suici- 
dal, or  homicidal  must  be  determined  by  the  coroner  or  medical  examiner 
and  the  registration  law  must  be  framed  to  harmonize. 


478  APPENDIX  III 

body  of  any  deceased  person  and  to  make  the  certificate  of  death 
required  for  a  burial  permit  shall  state  in  his  certificate  the  name  of  the 
disease  causing  death,  or  if  from  external  causes,  (1)  the  means  of  death 
and  (2)  whether  (probably)  accidental,  suicidal,  or  homicidal,  and  shall 
in  any  case  furnish  such  information  as  may  be  required  by  the  State 
Registrar  in  order  properly  to  classify  the  death. 

SEC.  9.  That  the  undertaker  or  person  acting  as  undertaker  shall  file 
the  certificate  of  death  with  the  local  registrar  of  the  district  in  which 
the  death  occurred  and  obtain  a  burial  or  removal  permit  prior  to  any 
disposition  of  the  body.  He  shall  obtain  the  required  personal  and 
statistical  particulars  from  the  person  best  qualified  to  supply  them, 
over  the  signature  and  address  of  his  informant.  He  shall  then  present 
the  certificate  to  the  attending  physician,  if  any,  or  to  the  health  officer 
or  coroner,  as  directed  by  the  local  registrar,  for  the  medical  certificate 
of  the  cause  of  death  and  other  particulars  necessary  to  complete  the 
record,  as  specified  in  sections  7  and  8.  And  he  shall  then  state  the 
facts  required  relative  to  the  date  and  place  of  burial  or  removal,  over 
his  signature  and  with  his  address,  and  present  the  completed  certificate 
to  the  local  registrar  in  order  to  obtain  a  permit  for  burial,  removal,  or 
other  disposition  of  the  body.  The  undertaker  shall  deliver  the  burial 
permit  to  the  person  in  charge  of  the  place  of  burial  before  interring  or 
otherwise  disposing  of  the  body,  or  shall  attach  the  removal  permit  to 
the  box  containing  the  corpse,  when  shipped  by  any  transportation 
company,  said  permit  to  accompany  the  corpse  to  its  destination, 

where,  if  within  the  State  of ,  it  shall  be  delivered  to  the  person 

in  charge  of  the  place  of  burial. 

[Every  person,  firm,  or  corporation  selling  a  casket  shall  keep  a  record 
showing  the  name  of  the  purchaser,  purchaser's  post-office  address, 
name  of  deceased,  date  of  death,  and  place  of  death  of  deceased,  which 
record  shall  be  open  to  inspection  of  the  State  Registrar  at  all  times. 
On  the  first  day  of  each  month  the  person,  firm,  or  corporation  selling 
caskets  shall  report  to  the  State  Registrar  each  sale  for  the  preceding 
month,  on  a  blank,  provided  for  that  purpose:  Provided,  however,  That 
no  person,  firm,  or  corporation  selling  caskets  to  dealers  or  undertakers 
only  shall  be  required  to  keep  such  record,  nor  shall  such  report  be 
required  from  undertakers  when  they  have  direct  charge  of  the  disposi- 
tion of  a  dead  body. 

Every  person,  firm,  or  corporation  selling  a  casket  at  retail,  and  not 
having  charge  of  the  disposition  of  the  body,  shall  inclose  within  the 
casket  a  notice  furnished  by  the  State  Registrar  calling  attention  to 
the  requirements  of  the  law,  a  blank  certificate  of  death,  and  the  rules 


APPENDIX  III  479 

and  regulations  of  the  State  board  of  health  concerning  the  burial  or 
other  disposition -of  a  dead  body.]1  s 

SEC.  10.  That  if  the  interment  or  other  disposition  of  the  body  is  to 
be  made  within  the  State,  the  wording  of  the  burial  or  removal  permit 
may  be  limited  to  a  statement  by  the  registrar,  and  over  his  signature, 
that  a  satisfactory  certificate  of  death  having  been  filed  with  him,  as 
required  by  law,  permission  is  granted  to  inter,  remove,  or  dispose 
otherwise  of  the  body,  stating  the  name,  age,  sex,  cause  of  death,  and 
other  necessary  details  upon  the  form  prescribed  by  the  State  registrar. 

SEC.  11.  That  no  person  in  charge  of  any  premises  on  which  inter- 
ments are  made  shall  inter  or  permit  the  interment  or  other  disposition 
of  any  body  unless  it  is  accompanied  by  a  burial,  removal,  or  transit 
permit,  as  herein  provided.  And  such  person  shall  indorse  upon  the 
permit  the  date  of  interment,  over  his  signature,  and  shall  return  all 
permits  so  indorsed  to  the  local  registrar  of  his  district  within  ten  days 
from  the  date  of  interment,  or  within  the  tune  fixed  by  the  local  board 
of  health.  He  shall  keep  a  record  of  all  bodies  interred  or  otherwise 
disposed  of  on  the  premises  under  his  charge,  in  each  case  stating  the 
name  of  each  deceased  person,  place  of  death,  date  of  burial  or  disposal, 
and  name  and  address  of  the  undertaker;  which  record  shall  at  all 
times  be  open  to  official  inspection:  Provided,  That  the  undertaker,  or 
person  acting  as  such,  when  burying  a  body  in  a  cemetery  or  burial 
ground  having  no  person  in  charge,  shall  sign  the  burial  or  removal 
permit,  giving  the  date  of  burial,  and  shall  write  across  the  face  of  the 
permit  the  words  "No  person  in  charge,"  and  file  the  burial  or  removal 
permit  within  ten  days  with  the  registrar  of  the  district  in  which  the 
cemetery  is  located. 

SEC.  12.  That  the  birth  of  each  and  every  child  born  in  this  State 
shall  be  registered  as  hereinafter  provided. 

SEC.  13.  That  within  ten  days  after  the  date  of  each  birth  there  shall 
be  filed  with  the  local  registrar  of  the  district  in  which  the  birth  occurred 
a  certificate  of  such  birth,  which  certificate  shall  be  upon  the  form 
adopted  by  the  State  board  of  health  with  a  view  to  procuring  a  full  and 
accurate  report  with  respect  to  each  item  of  information  enumerated 
in  section  14  of  this  act.2 

In  each  case  where  a  physician,  midwife,  or  person  acting  as  midwife 
was  hi  attendance  upon  the  birth,  it  shall  be  the  duty  of  such  physician, 

1  The  provisions  in  brackets  may  be  useful  in  States  in  which  many 
funerals  are  conducted  without  regular  undertakers. 

2  A  proviso  may  be  added  that  shall  require  the  registration,  or  noti- 
fication, at  a  shorter  interval  than  ten  days,  of  births  that  occur  in  cities. 


480  APPENDIX  III 

midwife,  or  person  acting  as  midwife  to  file  in  accordance  herewith  the 
certificate  herein  contemplated. 

In  each  case  where  there  was  no  physician,  midwife,  or  person  acting 
as  midwife  in  attendance  upon  the  birth,  it  shall  be  the  duty  of  the  father 
or  mother  of  the  child,  the  householder  or  owner  of  the  premises  where 
the  birth  occurred,  or  the  manager  or  superintendent  of  the  public  or 
private  institution  where  the  birth  occurred,  each  in  the  order  named, 
within  ten  days  after  the  date  of  such  birth,  to  report  to  the  local 
registrar  the  fact  of  such  birth.  In  such  case  and  in  case  the  physician, 
midwife,  or  person  acting  as  midwife,  in  attendance  upon  the  birth  is 
unable,  by  diligent  inquiry,  to  obtain  any  item  or  items  of  information 
contemplated  in  section  14  of  this  act,  it  shall  then  be  the  duty  of  the 
local  registrar  to  secure  from  the  person  so  reporting,  or  from  any  other 
person  having  the  required  knowledge,  such  information  as  will  enable 
him  to  prepare  the  certificate  of  birth  herein  contemplated,  and  it  shall 
be  the  duty  of  the  person  reporting  the  birth,  or  who  may  be  interro- 
gated in  relation  thereto,  to  answer  correctly  and  to  the  best  of  his 
knowledge  all  questions  put  to  him  by  the  local  registrar  which  may  be 
calculated  to  elicit  any  information  needed  to  make  a  complete  record 
of  the  birth  as  contemplated  by  said  section  14,  and  it  shall  be  the  duty 
of  the  informant  as  to  .any  statement  made  in  accordance  herewith  to 
verify  such  statement  by  his  signature,  when  requested  so  to  do  by  the 
local  registrar. 

SEC.  14.  That  the  certificate  of  birth  shall  contain  the  following 
items,  which  are  hereby  declared  necessary  for  the  legal,  social,  and 
sanitary  purposes  subserved  by  registration  records : * 

(1)  Place  of  birth,  including  State,  county,  township  or  town,  village, 
or  city.     If  in  a  city,  the  ward,  street,  and  house  number;  if  in  a  hospi- 
tal or  other  institution,  the.  name  of  the  same  to  be  given,  instead  of  the 
street  and  house  number. 

(2)  Full  name  of  child.     If  the  child  dies  without  a  name,  before  the 
certificate  is  filed,  enter  the  words  "  Died  unnamed."     If  the  living  child 
has  not  yet  been  named  at  the  date  of  filing  certificate  of  birth,  the  space 
for  "Full  name  of  child"  is  to  be  left  blank,  to  be  filled  out  subsequently 
by  a  supplemental  report,  as  hereinafter  provided. 

(3)  Sex  of  child. 

(4)  Whether  a  twin,  triplet,   or  other  plural  birth.     A  separate 
certificate  shall  be  required  for  each  child  in  case  of  plural  births. 

1  The  following  items  are  those  of  the  United  States  standard  certi- 
ficate of  birth,  approved  by  the  Bureau  of  the  Census. 


APPENDIX  III  .  481 

(5)  For  plural  births,  number  of  each  child  in  order  of  birth. 

(6)  Whether  legitimate  or  illegitimate.1 

(7)  Date  of  birth,  including  the  year,  month,  and  day. 

(8)  Full  name  of  father. 

(9)  Residence  of  father. 

(10)  Color  or  race  of  father. 

(11)  Age  of  father  at  last  birthday,  in  years. 

(12)  Birthplace  of  father;  at  least  State  or  foreign  country,  if  known. 

(13)  Occupation  of  father.     The  occupation  to  be  reported  if  engaged 
in  any  remunerative  employment,  with  the  statement  of  (a)  trade, 
profession,  or  particular  kind  of  work;    (6)  general  nature  of  industry, 
business,  or  establishment  in  which  employed  (or  employer). 

(14)  Maiden  name  of  mother. 

(15)  Residence  of  mother. 

(16)  Color  or  race  of  mother. 

(17)  Age  of  mother  at  last  birthday,  in  years. 

(18)  Birthplace  of  mother;    at  least  State  or  foreign  country,  if 
known. 

(19)  Occupation   of   mother.     The   occupation  to   be   reported   if 
engaged  in  any  remunerative  employment,  with  the  statement  of  (a) 
trade,  profession,  or  particular  kind  of  work;    (6)  general  nature  of 
industry,  business,  or  establishment  in  which  employed  (or  employer). 

(20)  Number  of  children  born  to  this  mother,  including  present  birth. 

(21)  Number  of  children  of  this  mother  living. 

(22)  The  certification  of  attending  physician  or  midwife  as  to  attend- 
ance at  birth,  including  statement  of  year,  month,  day  (as  given  in  item 
7),  and  hour  of  birth,  and  whether  the  child  was  born  alive  or  stillborn. 
This  certification  shall  be  signed  by  the  attending  physician  or  midwife, 
with  date  of  signature  and  address;  if  there  is  not  physician  or  midwife 
in  attendance,  then  by  the  father  or  mother  of  the  child,  householder, 
owner  of  the  premises,  or  manager  or  superintendent  of  public  or  private 
institution  where  the  birth  occurred,  or  other  competent  person,  whose 
duty  it  shall  be  to  notify  the  local  registrar  of  such  birth,  as  required  by 
section  13  of  this  act. 

(23)  Exact  date  of  filing  in  office  of  local  registrar,  attested  by  his 
official  signature,  and  registered  number  of  birth,  as  hereinafter  pro- 
vided. 

SEC.  15.  That  when  any  certificate  of  birth  of  a  living  child  is  pre- 
sented without  the  statement  of  the  given  name,  then  the  local  registrar 

1  This  question  may  be  omitted  if  desired,  or  provision  may  be  made 
so  that  the  identity  of  parents  will  not  be  disclosed. 


482  APPENDIX  III 

shall  make  out  and  deliver  to  the  parents  of  the  child  a  special  blank  for 
the  supplemental  report  of  the  given  name  of  the  child,  which  shall  be 
filled  out  as  directed,  and  returned  to  the  local  registrar  as  soon  as  the 
child  shall  have  been  named. 

SEC.  16.  That  every  physician,  midwife,  and  undertaker  shall,  with- 
out delay,  register  his  or  her  name,  address,  and  occupation  with  the 
local  registrar  of  the  district  in  which  he  or  she  resides,  or  may  hereafter 
establish  a  residence;  and  shall  thereupon  be  supplied  by  the  local 
registrar  with  a  copy  of  this  act,  together  with  such  rules  and  regulations 
as  may  be  prepared  by  the  State  registrar  relative  to  its  enforcement. 
Within  thirty  days  after  the  close  of  each  calendar  year  each  local 
registrar  shall  make  a  return  to  the  State  registrar  of  all  physicians, 
midwives,  or  undertakers  who  have  been  registered  hi  his  district 
during  the  whole  or  any  part  of  the  preceding  calendar  year:  Provided, 
That  no  fee  or  other  compensation  shall  be  charged  by  local  registrars 
to  physicians,  midwives,  or  undertakers  for  registering  their  names 
under  this  section  or  making  returns  thereof  to  the  State  registrar.1 

SEC.  17.  That  all  superintendents  or  managers,  or  other  persons  in 
charge  of  hospitals,  almshouses,  lying-in,  or  other  institutions,  public 
or  private,  to  which  persons  resort  for  treatment  of  diseases,  confinement, 
or  are  committed  by  prjocess  of  law,  shall  make  a  record  of  all  the  per- 
sonal and  statistical  particulars  relative  to  the  inmates  in  their  institu- 
tions at  the  date  of  approval  of  this  act,  which  are  required  in  the  forms 
of  the  certificates  provided  for  by  this  act,  as  directed  by  the  State 
registrar;  and  thereafter  such  record  shall  be,  by  them,  made  for  all 
future  inmates  at  the  time  of  their  admittance.  And  in  case  of  persons 
admitted  or  committed  for  treatment  of  disease,  the  physician  in  charge 
shall  specify  for  entry  in  the  record,  the  nature  of  the  disease,  and 
where,  in  his  opinion,  it  was  contracted.  The  personal  particulars  and 
information  required  by  this  section  shall  be  obtained  from  the  indi- 
vidual himself  if  it  is  practicable  to  do  so;  and  when  they  can  not  be  so 
obtained,  they  shall  be  obtained  in  as  complete  a  manner  as  possible 
from  relatives,  friends,  or  other  persons  acquainted  with  the  facts. 

SEC.  18.  That  the  State  registrar  shall  prepare,  print,  and  supply  to 
all  registrars  all  blanks  and  forms  used  in  registering,  recording,  and 
preserving  the  returns,  or  in  otherwise  carrying  out  the  purposes  of  this 
act;  and  shall  prepare  and  issue  such  detailed  instructions  as  may  be 
required  to  procure  the  uniform  observance  of  its  provisions  and  the 

1  This  section  may  be  omitted  if  deemed  expedient  and  the  duty  of 
supplying  instructions  may  be  assumed  by  the  State  officer. 


APPENDIX  III  483 

maintenance  of  a  perfect  system  of  registration;  and  no  other  blanks 
shall  be  used  than  those  supplied  by  the  State  registrar.  He  shall  care- 
fully examine  the  certificates  received  monthly  from  the  local  registrars, 
and  if  any  such  are  incomplete  or  unsatisfactory  he  shall  require  such 
further  information  to  be  supplied  as  may  be  necessary  to  make  the 
record  complete  and  satisfactory.  And  all  physicians,  midwives, 
informants,  or  undertakers,  and  all  other  persons  having  knowledge  of 
the  facts,  .are  hereby  required  to  supply,  upon  a  form  provided  by  the 
State  registrar  or  upon  the  original  certificate,  such  information  as  they 
may  possess  regarding  any  birth  or  death  upon  demand  of  the  State 
registrar,  in  person,  by  mail,  or  through  the  local  registrar:  Provided, 
That  no  certificate  of  birth  or  death,  after  its  acceptance  for  registration 
by  the  local  registrar,  and  no  other  record  made  in  pursuance  of  this  act, 
shall  be  altered  or  changed  in  any  respect  otherwise  than  by  amendments 
properly  dated,  signed,  and  witnessed.  The  State  registrar  shall 
further  arrange,  bind,  and  permanently  preserve  the  certificates  in  a 
systematic  manner,  and  shall  prepare  and  maintain  a  comprehensive 
and  continuous  card  index  of  all  births  and  deaths  registered;  said 
index  to  be  arranged  alphabetically,  in  the  case  of  deaths,  by  the  names 
of  decendents,  and  in  the  case  of  births,  by  the  names  of  fathers  and 
mothers.  He  shall  inform  all  registrars  what  .diseases  are  to  be  con- 
sidered infectious,  contagious,  or  communicable  and  dangerous  to  the 
public  .health,  as  decided  by  the  State  board  of  health,  in  order  that 
when  deaths  occur  from  such  diseases  proper  precautions  may  be  taken 
to  prevent  their  spread. 

If  any  cemetery  company  or  association,  or  any  church  or  historical 
society  or  association,  or  any  other  company,  society,  or  association, 
or  any  individual,  is  in  possession  of  any  record  of  births  or  deaths 
which  may  be  of  value  in  establishing  the  genealogy  of  any  resident  of 
this  State,  such  company,  society,  association,  or  individual  may  file 
such  record  or  a  duly  authenticated  transcript  thereof  with  the  State 
registrar,  and  it  shall  be  the  duty  of  the  State  registrar  to  preserve  such 
record  or  transcript  and  to  make  a  record  and  index  thereof  in  such  form 
as  to  facilitate  the  finding  of  any  information  contained  therein.  Such 
record  and  index  shall  be  open  to  inspection  by  the  public,  subject  to 
such  reasonable  conditions  as  the  State  registrar  may  prescribe.  If 
any  person  desires  a  transcript  of  any  record  filed  in  accordance  here- 
with, the  State  registrar  shall  furnish  the  same  upon  application,  to- 
gether with  a  certificate  that  it  is  a  true  copy  of  such  record,  as  filed  in 
his  office,  and  for  his  services  in  so  furnishing  such  transcript  and 
certificate  he  shall  be  entitled  to  a  fee  of  (ten  cents  per  folio)  (fifty  cents 


484  APPENDIX  III 

• 

per  hour  or  fraction  of  an  hour  necessarily  consumed  in  making  such 
transcript)  and  to  a  fee  of  twenty-five  cents  for  the  certificate,  which 
fees  shall  be  paid  by  the  applicant. 

SEC.  19.  That  each  local  registrar  shall  supply  blank  forms  of  certi- 
ficates to  such  persons  as  require  them.  Each  local  registrar  shall 
carefully  examine  each  certificate  of  birth  or  death  when  presented  for 
record  in  order  to  ascertain  whether  or  not  it  has  been  made  out  in 
accordance  with  the  provisions  of  this  act  and  the  instructions  of  the 
State  registrar;  and  if  any  certificate  of  death  is  incomplete  or  unsatis- 
factory, it  shall  be  his  duty  to  call  attention  to  the  defects  in  the  return, 
and  to  withhold  the  burial  or  removal  permit  until  such  defects  are 
corrected.  All  certificates,  either  of  birth  or  of  death,  shall  be  written 
legibly,  in  durable  black  ink,  and  no  certificate  shall  be  held  to  be  com- 
plete and  correct  that  does  not  supply  all  of  the  items  of  information 
called  for  therein,  or  satisfactorily  account  for  their  omission.  If  the 
certificate  of  death  is  properly  executed  and  complete,  he  shall  then 
issue  a  burial  or  removal  permit  to  the  undertaker;  provided,  that  in 
case  the  death  occurred  from  some  disease  which  is  held  by  the  State 
board  of  health  to  be  infectious,  contagious,  or  communicable  and 
dangerous  to  the  public  health,  no  permit  for  the  removal  or  other  dis- 
position of  the  body  shall  be  issued  by  the  registrar,  except  under  such 
conditions  as  may  be  prescribed  by  the  State  board  of  health.  If  a 
certificate  of  birth  is  incomplete,  the  local  registrar  shall  immediately 
notify  the  informant  and  require  him  to  supply  the  missing  items  of 
information  if  they  can  be  obtained.  He  shall  number  consecutively 
the  certificates  of  birth  and  death,  in  two  separate  series,  beginning 
with  number  1  for  the  first  birth  and  the  first  death  in  each  calendar 
year,  and  sign  his  name  as  registrar  in  attest  of  the  date  of  filing  in  his 
office.  He  shall  also  make  a  complete  and  accurate  copy  of  each  birth 
and  each  death  certificate  registered  by  him  in  a  record  book  supplied 
by  the  State  registrar,  to  be  preserved  permanently  in  his  office  as  the 
local  record,  in  such  manner  as  directed  by  the  State  registrar.  And 
he  shall,  on  the  tenth  day  of  each  month,  transmit  to  the  State  registrar 
all  original  certificates  registered  by  him  for  the  preceding  month.  And 
if  no  births  or  no  deaths  occurred  in  any  month,  he  shall,  on  the  tenth 
day  of  the  following  month,  report  that  fact  to  the  State  registrar,  on  a 
card  provided  for  such  purpose. 

SEC.  20.  That  each  local  registrar  shall  be  paid  the  sum  of  twenty-five 
cents  for  each  birth  certificate  and  each  death  certificate  properly  and 
completely  made  out  and  registered  with  him,  and  correctly  recorded 
and  promptly  returned  by  him  to  the  State  registrar,  as  required  by 


APPENDIX   III  485 

« 

this  act.1  And  iii  case  no  births  or  no  deaths  were  registered  during 
any  month,  the  local  registrar  shall  be  entitled  to  be  paid  the  sum  of 
twenty-five  cents  for  each  report  to  that  effect,  but  only  if  such  report 
be  made  promptly  as  required  by  this  act.  All  amounts  payable  to  a 
local  registrar  under  the  provisions  of  this  section  shall  be  paid  by  the 
treasurer  of  the  county  in  which  the  registration  district  is  located,  upon 
certification  by  the  State  registrar.  And  the  State  registrar  shall 
annually  certify  to  the  treasurers  of  the  several  counties  the  number  of 
births  and  deaths  properly  registered,  with  the  names  of  the  local 
registrars  and  the  amounts  clue  each  at  the  rates  fixed  herein.2 

SEC.  21.  That  the  State  registrar  shall,  upon  request,  supply  to  any 
applicant  a  certified  copy  of  the  record  of  any  birth  or  death  registered 
under  provisions  of  this  act,  for  the  making  and  certification  of  which 
he  shall  be  entitled  to  a  fee  of  fifty  cents,  to  be  paid  by  the  applicant. 
And  any  such  copy  of  the  record  of  a  birth  or  death,  when  properly 
certified  by  the  State  registrar,  shall  be  prima  facie  evidence  in  all 
courts  and  places  of  the  facts  therein  stated.  For  any  search  of  the 
files  and  records  when  no  certified  copy  is  made,  the  State  registrar 
shall  be  entitled  to  a  fee  of  fifty  cents  for  each  hour  or  fractional  part  of 
an  hour  of  time  of  search,  said  fee  to  be  paid  by  the  applicant.  And  the 
State  registrar  shall  keep  a  true  and  correct  account  of  all  fees  by  him 
received  under  these  provisions,  and  turn  the  same  over  to  the  State 
treasurer:  Provided,  That  the  State  registrar  shall,  upon  request  of  any 
parent  or  guardian,  supply,  without  fee,  a  certificate  limited  to  a  state- 
ment as  to  the  date  of  birth  of  any  child  when  the  same  shall  be  neces- 
sary for  admission  to  school,  or  for  the  purpose  of  securing  employment : 
And  provided  further,  That  the  United  States  Census  Bureau  may  obtain, 
without  expense  to  the  State,  transcripts,  or  certified  copies  of  births 
and  deaths  without  payment  of  the  fees  herein  prescribed. 

SEC.  22.  That  any  person,  who  for  himself  or  as  an  officer,  agent,  or 
employee  of  any  other  person,  or  of  any  corporation  or  partnership  (a) 
shall  inter,  cremate,  or  otherwise  finally  dispose  of  the  dead  body  of  a 
human  being,  or  permit  the  same  to  be  done,  or  shall  remove  said  body 
from  the  primary  registration  district  in  which  the  death  occurred  or 

1  A  proviso  may  be  inserted  at  this  point  relative  to  fees  of  city 
registrars  who  are  already  compensated  by  salary  for  their  services. 
See  laws  of  Missouri,  Ohio,  and  Pennsylvania. 

2  Provision  may  be  made  in  this  section  for  the  payment  of  sub- 
registrars  and  also,  if  desired,  for  the  payment  of  physicians  and  mid- 
wives.     See  Kentucky  law. 


486  APPENDIX  III 

the  body  was  found  without  the  authority  of  a  burial  or  removal  permit 
issued  by  the  local  registrar  of  the  district  in  which  the  death  occurred 
or  in  which  the  body  was  found;  or  (6)  shall  refuse  or  fail  to  furnish 
correctly  any  information  in  his  possession,  or  shall  furnish  false  in- 
formation affecting  any  certificate  or  record,  required  by  this  act;  or 
(c)  shall  willfully  alter,  otherwise  than  is  provided  by  section  18  of  this 
act,  or  shall  falsify  any  certificate  of  birth  or  death,  or  any  record 
established  by  this  act;  or  (d)  being  required  by  this  act  to  fill  out  a 
certificate  of  birth  or  death  and  file  the  same  with  the  local  registrar, 
or  deliver  it,  upon  request,  to  any  person  charged  with  the  duty  of  filling 
the  same,  shall  fail,  neglect,  or  refuse  to  perform  such  duty  in  the 
manner  required  by  this  act;  or  (e)  being  a  local  registrar,  deputy 
registrar,  or  subregistrar,  shall  fail,  neglect,  or  refuse  to  perform  his 
duty  as  required  by  this  act  and  by  the  instructions  and  direction  of  the 
State  registrar  thereunder,  shall  be  deemed  guilty  of  a  misdemeanor, 
and  upon  conviction  thereof  shall  for  the  first  offense  be  fined  not  less 
than  five  dollars  ($5)  nor  more  than  fifty  dollars  ($50),  and  for  each 
subsequent  offense  not  less  than  ten  dollars  ($10)  nor  more  than  one 
hundred  dollard  ($100),  or  be  imprisoned  in  the  county  jail  not  more  than 
sixty  days,  or  be  both  fined  and  imprisoned  in  the  discretion  of  the 
court.1 

SEC.  23.  That  each  local  registrar  is  hereby  charged  with  the  strict 
and  thorough  enforcement  of  the  provisions  of  this  act  in  his  registration 
district,  under  the  supervision  and  direction  of  the  State  registrar. 
And  he  shall  make  an  immediate  report  to  the  State  registrar  of  any 
violation  of  this  law  coming  to  his  knowledge,  by  observation  or  upon 
complaint  of  any  person  or  otherwise. 

The  State  registrar  is  hereby  charged  with  the  thorough  and  efficient 
execution  of  the  provisions  of  this  act  in  every  part  of  the  State,  and  is 
hereby  granted  supervisory  power  over  local  registrars,  deputy  local 
registrars,  and  subregistrars  to  the  end  that  all  of  its  requirements  shall 
be  uniformly  complied  with.  The  State  registrar,  either  personally  or 
by  an  accredited  representative,  shall  have  authority  to  investigate 
cases  of  irregularity  or  violation  of  law,  and  all  registrars  shall  aid  him 
upon  request,  in  such  investigations.  When  he  shall  deem  it  necessary 
he  shall  report  cases  of  violation  of  any  of  the  provisions  of  this  act  to 
the  prosecuting  attorney  of  the  county,  with  a  statement  of  the  facts 

1  Provision  may  be  made  whereby  compliance  with  this  act  shall 
constitute  a  condition  of  granting  licenses  to  physicians,  midwives,  and 
embalmers. 


APPENDIX  III  487 

and  circumstances;  and  when  any  such  case  is  reported  to  him  by  the 
State  registrar  the  prosecuting  attorney  shall  forthwith  initiate  and 
promptly  follow  up  the  necessary  court  proceedings  against  the  person 
Dr  corporation  responsible  for  the  alleged  violation  of  law.  And  upon 
request  of  the  State  registrar,  the  attorney  general  shall  assist  in  the 
anforcement  of  the  provisions  of  this  act. 

NOTE.  —  Other"  sections  should  be  added  giving  the  date  on  which 
the  act  is  to  go  into  effect,  if  not  determined  by  constitutional  provisions 
Df  the  State;  providing  for  the  financial  support  of  the  law;  and  repeal- 
ing prior  statutes  inconsistent  with  the  present  act. 

It  is  desirable  that  the  entire  bill  should  be  reviewed  by  competent 
legal  authority  for  the  purpose  of  discovering  whether  it  can  be  made 
more  consistent  in  any  respect  with  the  general  form  of  legislation  of 
ihe  State  in  which  the  bill  is  to  be  introduced,  without  material  change 
Dr  injury  to  the  effectiveness  of  registration. 

THE  STANDARD  BIRTH  AND  DEATH  CERTIFICATES 

The  following  are  facsimile  reproductions  of  the  standard  birth  and 
death  certificates.  They  have  been  reduced  in  size  to  meet  the  require- 
ments of  the  printed  page.  The  size  of  the  birth  certificate  is  6|  by 
7|  inches,  and  of  the  death  certificate  7j  by  8|  inches.  Copies  can  be 
Dbtained  from  the  Director  of  the  Census  upon  request. 


488 


APPENDIX  III 


UNITED   STATES   STANDARD   CERTIFICATE   OF  BIRTH 


(Instructions  on  certain  points  may  be  printed  on  the  back  Size  of  certificate,  6|  X  7$  inches.) 
^MARGIN  RESERVED  FOR  BINDING 
V.  S.  No.  109  WRITE  PLAINLY,  WITH  UNFADING  INK  —  THIS  IS  A  PERMANENT  RECORD 

N.  B.  —  In  case  of  more  than  one  child  at  a  birth,  a  SEPARATE  RETURN  must  be  made 
for  each,  and  the  number  of  each,  in  order  of  birth,  stated 

PLACE  OF  BIRTH             DEPAR 
County  of                            STAN  DA 

TMENT  OF  COMMERCE  AND  LABOR 
BUREAU  OF  THE  CENSUS 

RD  CERTIFICATE  OF  BIRTH 
Registered  No  

Township  of 

Village  of  
or 
City  of  (No  ,  . 

FULL   NAME   OF   CHILD 

St.;  Ward) 

(  If  child  is  not  yet  named,  make 
isnnnlfimentnl  rpnnrt,  as  directed 

Sex  of       Twin,  triplet,       Number  in  order     Legiti-        Date  of  birth 
Child           or  other?              of  birth                  mate?       ,  19.. 

(To  b«  answered  only  in  ey.nt  of  plnr.1  births,                               (Month)     (D»y)     (Year) 

FATHER 
FULL 
NAME 

MOTHER 
FULL 
MAIDEN 
NAME 

RESIDENCE 

RESIDENCE 

COLOR                          AGE  AT  LAST 
BIRTHDAY  

(Years) 

COLOR                        AGE   AT   LAST 
BIRTHDAY      

(Yeari) 

BIRTHPLACE 

BIRTHPLACE 

OCCUPATION 

OCCUPATION 

Number  of  children  born  to  this 
mother,  including  present  birth.  .  . 

Number  of  children  of  this  mother 
now  living  

CERTIFICATE  OF  ATTENDING 

I  hereby  certify  that  I  attended 
at           M  ,    on 

PHYSICIAN   OR   MIDWIFE  1 

the   birth  of  this  child,  who  was 
the  date  above  stated. 

an      (Signature)                                 . 

(Born  alive  or  Stillborn) 

1  When  there  was  no  attending  physic 
or  midwife,  then  the  father,  household 
etc.,  should  make  this  return.     A  stillbt 
child  is  one  that  neither  breathes  nor  sho 
other  evidence  of  life  after  birth. 

Given  name  added  from  a  supplemei 
report  , 

er, 
rrn                         

WS                               (Physician  or  Midwife) 

ital    Address  

19 
Filed  19     

Begjrtrar 

APPENDIX  III 


489 


MARGIN  RESERVED  FOR  BINDING 
This  supplemental  report  is  to  be  pasted  be- 
8-442  neath  the  original 

V.  S.  No.  108 

SUPPLEMENTAL  REPORT  OF  BIRTH 

(STATE) 
(This  return  should  preferably  be  made  by  the  person  who  made  the  original  ) 
Registered  Number  l  

Place  of  birth  l                               No  St. 

(R«Ci*tratioi>  district) 

I  HEREBY  CERTIFY  that  the 
child  described  herein 
has  been  named: 

SEX  of    Twin.i        '           Number  i, 
CHILD  i    triplet,          and<in  order 
or  other?     J          01  birth 

DATE  OF  BIRTH  l  190.  . 

(Month)        (Day)         (Year) 

(GiT«  name  in  fall)              (Surnwn*) 

(Signature)           

FULL  1                             FATHER 
NAME 

FULL  1                             MOTHER 
MAJDEN   . 
NAME 

(Phjiioian  or  midwife) 
11-3 

i  These  items  to  be  entered  by  the 
Registrar  before  giving  out  this  form. 

490 


APPENDIX  III 


III 


581 


«  ss 
g  ^ 

gag 


55  iSts 

KH  •-•   W    <tf 

O  4)  ^ 

i  O^w 

3  5s  . 


. 

31! 
01  £ 


DEPARTMENT  OF   COMMERCE 
BUREAU   OF  THE    CENSUS 

STANDARD   CERTIFICATE   OF  DEATH 

»  PLACE  OF  DEATH 

County State Registered  No 

Township or  Village or 

City No , , St.,. . . ...  .Ward 


ith  occurred  in  a  hospital  or  institution, 
give  its  NAME  instead  of  street  and  number.) 

a  FULL   NAME 

(a)  Residence.    No St.,. . .  .Ward 

(Usual  place  of  abode.)      (If  nonresident  give  city  or  town  and  State.) 

Length  of  residence  in  city  or  town  How  long  in  U.  S.,  if  of  for- 

where  death  occurred,    yrs.    mos.    ds.        eign  birth?    yrs.    mos.    ds. 


•ERSONALAND  STATISTICAL  PARTICULARS 


*  COLOR 
OR  RACE 


s  Single,  Married, 

Widowed, 

Divorced 

(Write  the  word) 


If  married,  widowed,  or  divorced 
HUSBAND  of 
(or)  WIFE  of 


6  DATE  OF  BIRTH  (month,  day,  and 
year) 


^  AGE  Yrs. 


Mo.s. 


Ds. 


If  LESS  than 
1  day, . . .  hrs. 


8  OCCUPATION  OF  DECEASED 

(a)  Trade,  profession,  or 
particular  kind  of  work 

(b)  General  nature  of  industry, 
business,    or    establishment     in 
which  employed  (or  employer) . . . 

(c)  Name  of  employer .  '. 


9  BIRTHPLACE  (city  or  town) 

(State  or  country) 


10  NAME   OF   FATHER 


11  BIRTHPLACE  OF   FATHER  (city 

town) 

(State  or  country) 


12  MAIDEN  NAME  OF  MOTHER 


13  BIRTHPLACE  OF  MOTHER  (city  Or 

town) - 

(State  or  country) 


i*  Informant 

(Address) 


15  Filed.. 


Registrar 


MEDICAL  CERTIFICATE  OF  DEATH 


i«  DATE  OF  DEATH  (month,  day,  and 
year)  19 


I  HEREBY  CERTIFY,  That 
I  attended  deceased  from 

,  19 to ,  19.. 

that  I  last  saw  h ...  alive  on 19.. 

and  that  death  occurred,  on  the 

date  stated  above,  at m. 

The  CAUSE  OF  DEATH*  was  as  follows: 


(duration) . .  .yrs mos. . .  ds. 

CONTRIBUTORY 

(Secondly) 

(duration)... yrs..  .mos..  .ds. 

i8  Where  was  disease  contracted 

if  not  at  place  of  death? 

Did  an  operation  precede  death? 

Date  of 

Was  there  an  autopsy? 

What  test  confirmed  diagnosis? 

(Signed) ,  M.D. 

,  19      (Address) 


*  State  the  Disease  Causing  Death, 
or  in  deaths  from  Violent  Causes, 
state  (1)  Means  and  Nature  of  In- 
jury;  and  (2)  whether  Accidental, 
Suicidal,  or  Homicidal.  (See  reverse 
side  for  additional  space.) 


9  PLACE  OF  BURIAL, 
CREMATION,  OR  RE- 
MOVAL 


20  UNDERTAKER 


DATE  OF  BURIAL 


19 


L 


APPENDIX  IV. 

TABLE  VL— LOGARITHMS  OF  NUMBERS. 


N 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

100 

00000  00043  00087 

00130 

00173  00217  00260 

00303 

00346  00389 

1 

0432 

0475 

0518 

0561 

0604 

0647 

0689 

0732 

0775 

0817 

2 

0860 

0903 

0945 

0988 

1030 

1072 

1115 

1157 

1199 

1242 

3 

1284 

1326 

1368 

1410 

1452 

1494 

1536 

1578 

1620 

1662 

4 

1703 

1745 

1787 

1828 

1870 

1912 

1953 

1995 

2036 

2078 

5 

2119 

2160 

2202 

2243 

2284 

2325 

2366 

2407 

2449 

2490 

6 

2531 

2572 

2612 

2653 

2694 

2735 

2776 

2816 

2857 

2898 

7 

2938 

2979 

3019 

3060 

3100 

3141 

3181 

3222 

3262 

3302 

8 

3342 

3383 

3423 

3463 

3503 

3543 

3583 

3623 

3663 

3703 

9 

3743 

3782 

3822 

3862 

3902 

3941 

3981 

4021 

4060 

4100 

110 

04139  04179  04218  04258  04297  04336  04376  04415 

04454 

04493 

1 

4532 

4571 

4610 

4650 

4689 

4727 

4766 

4805 

4844 

4883 

2 

4922 

4961 

4999 

6038 

5077 

5115 

5154 

5192 

6231 

5269 

3 

5308 

5346 

5385 

5423 

5461 

5500 

5538 

5576 

5614 

5652 

4 

5690 

5729 

5767 

5805 

5843 

5881 

6918 

5956 

5994 

6032 

5 

6070 

6108 

6145 

6183 

6221 

6258 

6296 

6333 

6371 

6408 

6 

6446 

6483 

6521 

6558 

6595 

6633 

6670 

6707 

6744 

6781 

7 

6819 

6856 

6893 

6930 

6967 

7004 

7041 

7078 

7115 

7151 

8 

7188 

7225 

7262 

7298 

7335 

7372 

7408 

7446 

7482 

7518 

9 

7551 

7591 

7628 

7664 

7700 

7737 

7773 

7809 

7846 

7882 

120 

07918  07954  07990  08027  08063  08099  08135  08171 

08207 

08243 

1 

8279 

8314 

8350 

8386 

8422 

8458 

8493 

8529 

8565 

8600 

2 

8636 

8672 

8707 

8743 

8778 

8814 

8849 

8884 

8920 

8966 

3 

8991 

9026 

9061 

9096 

9132 

9167 

9202 

9237 

9272 

9307 

4 

9342 

9377 

9412 

9447 

9482 

9517 

9552 

9587 

9621 

9666 

5 

9691 

9726 

9760 

9795 

9830 

9864 

9899 

9934 

9968 

10003 

6 

10037 

10072 

10106 

10140 

10175 

10209 

10243  10278 

10312 

0346 

7 

0380 

041^ 

0449 

0483 

0517 

0551 

0585 

0619 

0653 

0687 

8 

0721 

0755 

0789 

0823 

0857 

0890 

0924 

0958 

0992 

1025 

9 

1059 

1093 

1126 

1160 

1193 

1227 

1261 

1294 

1327 

1361 

130 

11394 

11428 

11461 

11494 

11528 

11561 

11594 

11628 

11661 

11694 

1 

1727 

1760 

1793 

1826 

1860 

1893 

1926 

1959 

1992 

2024 

2 

2057 

2090 

2123 

2156 

2189 

2222 

2254 

2287 

2320 

2352 

3 

2385 

2418 

2450 

2483 

2516 

2548 

2581 

2613 

2646 

2678 

4 

2710 

2743 

2775 

2808 

2840 

2872 

2905 

2937 

2969 

3001 

5 

3033 

3066 

3098 

3130 

3162 

3194 

3226 

3258 

3290 

3322 

6 

3354 

3386 

3418 

3450 

3481 

3513 

3545 

3577 

3609 

3640 

7 

-3672 

3704 

3735 

3767 

3799 

3830 

3862 

3893 

3925 

3956 

8 

3988 

4019 

4051 

4082 

4114 

4145 

4176 

4208 

4239 

4270 

9 

4301 

4333 

4364 

4395 

4426 

4457 

4489 

4520 

4551 

4582 

UO 

14613 

14644 

14675 

14706 

14737 

14768 

14799 

14829 

14860 

14891 

1 

4922 

4953 

4983 

5014 

5045 

5076 

5106 

5137 

5168 

5198 

2 

5229 

5259 

5290 

5320 

5351 

5381 

5412 

5442 

5473 

5503 

3 

5534 

5564 

5594 

5625 

5655 

5685 

5715 

5746 

6776 

5806 

4 

5836 

5866 

5897 

5927 

6957 

5987 

6017 

6047 

6077 

6107 

5 

6137 

6167 

6197 

6227 

6256 

6286 

6316 

6346 

6376 

6406 

6 

6435 

6465 

6495 

6524 

6554 

6584 

6613 

6643 

6673 

6702 

7 

6732 

6761 

6791 

6820 

6850 

6879 

6909 

6938 

6967 

6997 

8 

7026 

7056 

7085 

7114 

7143 

7173 

7202 

7231 

7260 

7289 

9 

7319 

7348 

7377 

7406 

7435 

7464 

7493 

7522 

7551 

7580 

150 

17609 

17638 

17667 

17696 

17725 

17754 

17782 

17811 

17840 

17869 

491 


492  TABLE  VI.— LOGARITHMS   OF   NUMBERS. 


N0123456789 


150 

1 
2 
3 
4 
5 
6 
7 
8 
9 

160 

1 
2 
3 
4 
5 
6 
7 
8 
9 

170 

1 
2 
3 
4 
5 
6 
7 
8 
9 

180 
1 
2 
3 

4 
5 
6 
7 
8 


190 

1 
2 
3 
4 
5 
6 
7 
8 
9 

200 


17609  17638  17667  17696  17725  17754  17782  17811  17840  17869 

7898  7926  7955  7984  8013  8041  8070  8099  8127  8156 

8184  8213  8241  8270  8298  8327  8355  8384  8412  8441 

8469  8498  8526  8554  8583  8611  8639  8667  8696  8724 

8752  8780  8808  8837  8865  8893  8921  8949  8977  9005 

9033  9061  9089  9117  9145  9173  9201  9229  9257  9285 

9312  9340  9368  9396  9424  9451  9479  9507  9535  9562 

9590  9618  9645  9673  9700  9728  9756  9783  9811  9838 

9866  9893  9921  9948  9976  20003  20030  20058  20085  20112 

2014020167201942022220249  0276  0303  0330  0358  0385 

20412  20439  20466  20493  20520  20548  20575  20602  20629  20656 

0683  0710  0737  0763  0790  0817  0844  0871  0898  0925 

0952  0978  1005  1032  1059  1085  1112  1139  1165  1192 

1219  1245  1272  1299  1325  1352  1378  1403  1431  1458 

1484  1511  1537  1564  1590  1617  1643  1669  1696  1722 

1748  177^  1801  1827  1854  1880  1906  1932  1958  1985 

2011  2037  2063  2089  2115  2141  2167  2194  2220  2246 

2272  2298  2324  2350  2376  •  2401  2427  2453  2479  2505 

2531  2557  2583  2608  2634  2660  2686  2712  2737  2763 

2789  2814  2840  2866  2891  2917  2943  2968  2994  3019 

23045  23070  23096  23121  23147  23172  23198  23223  23249  23274 

3300  3325  3350  3376  3401  3426  3452  3477  3502  3528 

3553  3578  3603  3629  3654  3679  3704  3729  3754  3779 

3805  3830  3855  3880  3905  3930  3955  3980  4005  4030 

4055  4080  4105  4130  4155  4180  4204  4229  4254  4279 

4304  4329  4353  4378  4403  4428  4452  4477  4502  4527 

4551  4576  4601  4625  4650  4674  4699  4724  4748  4773 

4797  4822  4846  4871  4895  4920  4944  4969  4993  5018 

5042  5066  5091  5115  5139  5164  5188  5212  5237  5261 

5285  5310  5334  5358  5382  5406  5431  5455  5479  5503 

25527  25551  25575  25600  25624  25648  25672  25696  25720  25744 

5768  5792  5816  5840  5864  5888  5912  5935  5959  5983 

6007  6031  6055  6079  6102  6126  6150  6174  6198  6221 

6245  6269  6293  6316  6340  6364  6387  6411  6435  6458 

6482  6505  6529  6553  6576  6600  6623  6647  6670  6694 

6717  6741  6764  6788  6811  6834  6858  6881  6905  6928 

6951  6975  6998  7021  7045  7068  7091  7114  7138  7161 

7184  7207  7231  7254  7277  7300  7323  7346  7370  7393 

7416  7439  7462  7485  7508  7531  7554  7577  7600  7623 

7646  7669  7692  7715  7738  7761  7784  7807  7830  7852 

27875  27898  27921  27944  27967  27989  28012  28035  28058  28081 

8103  8126  8149  8171  8194  8217  8240  8262  8285  8307 

8330  8353  8375  8398  8421  8443  8466  8488  8511  8533 

8556  8578  8601  8623  8646  8668  8691  8713  8735  8758 

8780  8803  8825  8847  8870  8892  8914  8937  8959  8981 

9003  9026  9048  9070  9092  9115  9137  9159  9181  9203 

9226  9248  9270  9292  9314  9336  9358  9380  9403  9425 

9447  9469  9491  9513  9535  9557  9579  9601  9623  9645 

9667  9688  9710  9732  9754  9776  9798  9820  9842  9863 

9885  9907  9929  '9951  9973  9994  30016  30038  30060  30081 

30103  30125  30146  30168  30190  30211  30233  30255  30276  30298 


TABLE  VI.— LOGARITHMS  OF  NUMBERS.  493 


NO123456789 


200 
1 
9 
3 
4 
5 
6 
7 
8 
9 

210 

1 
2 
3 
4 
5 
6 
7 
8 
9 

220 

1 
2 
3 
4 
5 
6 
7 
8 


230 

1 
2 
3 
4 
5 
6 
7 
8 
9 

240 

1 
2 
3 
4 
5 
6 
7 
8 
9 


30103  30125  30146  30168  30190  30211  30233  30255  30276  30298 

0320  0341  0363  0384  0406  0428  0449  0471  0492  0514 

0535  0557  0578  0600  0621  0643  0664  0685  0707  0728 

0750  0771  0792  0814  0835  0856  0878  0899  0920  0942 

0963  0984  1006  1027  1048  1069  1091  1112  1133  1154 

1175  1197  1218  1239  1260  1281  1302  1323  1345  1366 

1387  1408  1429  1450  1471  1492  1513  1634  1555  1576 

1597  1618  1639  1660  1681  1702  1723  1744  1765  1786 

1806  1827  1848  1869  1890  1911  1931  1952  1973  1994 

2015  2035  2056  2077  2098  2118  2139  2160  2181  2201 

32222  32243  32263  32284  32305  32325  32346  32366  32387  32408 

2428  2449  2469  2490  2510  2531  2552  2572  2593  2613 

2634  2654  2675  2695  2715  2736  2756  2777  2797  2818 

2838  2858  2879  2899  2919  2940  2960  2980  3001  3021 

3041  3062  3082  3102  3122  3143  3163  3183  3203  3224 

3244  3264  3284  3304  3325  3345  3365  3385  3405  3425 

3445  3465  3486  3506  3526  3546  3666  3586  3606  3626 

3646  3666  3686  3706  3726  3746  3766  3786  3806  3826 

3846  3866  3885  3905  3925  3945  3965  3985  4005  4025 

4044  4064  4084  4104  4124  4143  4163  4183  4203  4223 

34242  34262  34282  34301  34321  34341  34361  34380  34400  34420 

4439  4459  4479  4498  4518  4537  4557  4577  4696  4616 

4635  4655  4674  4694  4713  4733  4753  4772  4792  4811 

4830  4850  4869  '4889  4908  4928  4947  4967  4986.  6005 

5025  5044  5064  5083  5102  6122  5141  6160  5180  5199 

5218  6238  6257  5276  5295  5315  5334  5353  6372  6392 

5411  5430  5449  5468  5488  6507  5526  6545  6564  5683 

5603  5622  5641  5660  5679  5698  5717  6736  6755  5774 

5793  5813  5832  5851  5870  6889  5908  5927  5946  6965 

5984  6003  6021  6040  6059  6078  6097  6116  6135  6154 

36173  36192  36211  36229  36248  36267  36286  36305  36324  36342 

6361  6380  6399  6418  6436  6455  6474  6493  6511  6630 

6549  6568*  6586  6605  6624  6642  6661  6680  6698  6717 

6736  6754  6773  6791  6810  6829  6847  6866  6884  6903 

6922  6940  6959  6977  6996  7014  7033  7051  7070  7088 

71C7  7125  7144  7162  7181  7199  7218  7236  7254  7273 

7291  7310  7328  7346  7365  7383  7401  7420  7438  7457 

7475  7493  7511  7530  7548  7566  7585  7603  7621  7639 

7658  7676  7694  7712  7731  7749  7767  7785  7803  7822 

7840  7858  7876  7894  7912  7931  7949  7967  7985  8003 

38021  38039  38057  38075  38093  38112  38130  38148  38166  38184 

8202  8220  8238  8256  8274  8292  8310  8328  8346  8364 

8382  8399  8417  8435  8453  8471  8489  8507  8525  8543 

8561  8578  8596  8614  8632  8650  8668  8686  8703  8721 

8739  8757  8775  8792  8810  8828  8846  8863  8881  8899 

8917  8934  8952  8970  8987  9005  9023  9041  9058  9076 

9094  9111  9129  9146  9164  9182  9199  9217  9235  9252 

9270  9287  9305  9322  9340  9358  9375  9393  9410  9428 

9445  9463  9480  9498  9515  9533  9550  9568  9585  9602 

9620  9637  9655  9672  9690  9707  9724  9742  9759  9777 


250  39794  39811  39829  39846  39863  39881  39898  39916  39933  39950 


494 


TABLE  VI.— LOGARITHMS  OF  NUMBKKtf. 


6 


8       9 


250 
1 
2 
3 

4 
5 
6 

7 
8 
9 

260 

1 
2 
3 
4 
5 
6 
7 
8 
9 

270 

1 
2 
3 
4 
5 
6 
7 
8 
9 

280 

1 
2 
3 
4 
5 
6 
7 
8 
9 

290 

1 
2 

3 

4 
5 
6 
7 
8 
9 


39794 
9967 

40140 
0312 
0483 
0654 
0824 
0993 
1162 
1330 


39811  39829 
9985  40002 

40157  0175 
0329  0346 
0500  0518 
0671  0688 
0841  0858 
1010  1027 
1179  1196 
1347  1363 


39846  39863  39881 
40019  40037  40054 
0192  0209  0226 
0364  0381  0398 
053^  0552  0569 
0705  0722  0739 
0875  0892  0909 
1044  1061  1078 
1212  1229  1246 
1380  1397  1414 


39898  39915  39933  39950 
40071  40088  40106  40123 
0243  0261  0278  0295 
0415  0432  0449  0466 
0586  0603  0620  0637 
0756  0773  0790  0807 
0926  0943  0960  0976 
1095  1111  1128  1145 
1263  1280  1296  1313 
1430  1447  1464  1481 


41497  41514 

1664  1681 

1830  1847 

1996  2012 

2160  2177 

2325  2341 

2488  2504 

2651  2667 

2813  2830 

2975  2991 

43136  43152 

3297  3313 

3457  3473 

3616  3632 

3775  3791 

3933  3949 

4091  4107 

4248  4264 

4404  4420 

4560  4576 


41531 
1697 
1863 
2029 
2193 
2357 
2521 
2684 
2846 
3008 


41547 
1714 
1880 
20  i5 
2210 
2374 
2537 
2700 
2862 
3024 


44716 
4871 
5025 
5179 
5332 
5484 
5637 
5788 
5939 
6090 

46240 


6538 
6687 
6835 
6982 
7129 
7276 
7422 
7567 


44731 
4886 
5040 
5194 
5347 
5500 
5652 
5803 
5954 
6105 

46255 
6404 
6553 
6702 
6850 
6997 
7144 
7290 
7436 
7582 


43169  43185 

3329  3345 

3489  3505 

3648  3664 

3807  3823 

3965  3981 

4122  4138 

4279  4295 

4436  4451 

4592  4607 

44747  44762 

4902  4917 

5056  5071 

5209  5225 

5362  5378 

5515  5530 

5667  5682 

5818  5834 

5969  5984 

6120  6135 

46270  46285 

6419  6434 

6568  6583 

6716  6731 

6864  6879 

7012  7026 

7159  7173 

7305  7319 

7451  7465 

7596  7611 


41564 
1731 
1896 
2062 
2226 
-2390 
2553 
2716 
2878 
3040 

43201 
3361 
3521 


3838 
3996 
4154 
4311 
4467 
4623 

44778 
4932 
5086 
5240 
5393 
5545 
5697 
5849 
6000 
6150 


41581 
1747 
1913 
2078 
2243 
2406 
2570 
2732 
2894 
3056 

43217 

3377 
3537 
3696 
3854 
4012 
4170 
4326 
4483 
4638 

44793 
4948 
5102 
5255 
5408 
5561 
5712 
5864 
6015 
6165 


41597 
1764 
1929 
2095 
2259 
2423 
2586 
2749 
2911 
3072 

43233 
3393 
3553 
3712 
3870 
4028 
4185 
4342 
4498 
4654 


41614 
1780 
1946 
2111 
2275 
2439 
2602 
2765 
2927 
3088 


41631 
1797 
1963 
2127 
2292 
2455 
2619 
2781 
2943 
3104 


43249  43265 

3409  3425 

3569  3584 

3727  3743 

3886  3902 

4044  4059 

4201  4217 

4358  4373 

4514  4529 

4669  4685 


46300  46315 

6449  6464 

6598  6613 

6746  6761 

6894  6909 

7041  7056 

7188  7202 

7334  7349 

7480  7494 

7625  7640 


44809  44824 

4963  4979 
5111  5133 

5271  5286 

5423  5439 

5576  5591 

5728  5743 

5879  5894 

6030  6045 

6180  6195 

46330  46345 

6479  6494 

6627  6642 

6776  6790 

6923  6938 

7070  7085 

7217  7232 

7363  7378 

7509  7524 

7654  7669 


44840 
4994 
5148 
5301 
5454 
5606 
5758 
5909 
6060 
6210 


41647 
1814 
1979 
2144 
2308 
2472 
2635 
2797 
2959 
3120 

43281 
3441 
3600 
3759 
3917 
4075 
4232 
4389 
4545 
4700 

44855 
5010 
5163 
5317 
5469 
5621 
5773 
5924 
6075 
6225 


46359  46374 

6509  6523 

6657  6672 

6805  6820 

6953  6967 

7100  7114 

7246  7261 

7392  7407 

7538  7553 

7683  7698 


300  47712  47727  47741  47756  47770  47784  47799  47813  47828  47842 


TABLE  VI.— LOGARITHMS  OF   NUMBERS. 


495 


N 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

BOO 

47712  47727 

47741 

47756  47770 

47784 

47799 

47813 

47828  47842 

1 

7857 

7871 

7885 

7900 

7914 

7929 

7943 

7958 

7972 

7986 

2 

8001 

8015 

8029 

8044 

8058 

8073 

8087 

8101 

8116 

8130 

3 

8144 

8159 

8173 

8187 

8202 

8216 

8230 

8244 

8259 

8273 

4 

8287 

8302 

8316 

8330 

8844 

8359 

8373 

8387 

8401 

8416 

5 

8430 

8444 

8458 

8473 

8487 

8501 

8515 

8530 

8544 

8558 

6 

8572 

8586 

8601 

8615 

8629 

8643 

8657 

8671 

8686 

8700 

7 

8714 

8728 

8742 

8756 

8770 

8785 

8799 

8813 

8827 

8841 

8 

8855 

8869 

8883 

8897 

8911 

8926 

8940 

8954 

8968 

8982 

9 

8996 

9010 

9024 

9038 

9052 

9066 

9080 

9094 

9108 

9122 

310 

49136 

49150 

49164  49178 

49192 

49206  49220  49234  49248  49262 

1 

9276 

9290 

9304 

9318 

9332 

9346 

9360 

9374 

9388 

9402 

2 

9415 

9429 

9443 

9457 

9471 

9485 

9499 

9513 

9527 

9541 

3 

9554 

9568 

9582 

9596 

9610 

9624 

9638 

9651 

9665 

9679 

4 

9693 

9707 

9721 

9734 

9748 

9762 

9776 

9790 

9803 

9817 

5 

9831 

9845 

9859 

9872 

9886 

9900 

9914 

9927 

9941 

9955 

6 

9969 

9982 

9996  50010 

50024 

50037 

50051 

50065 

50079  50092 

7 

50106 

50120 

50133 

0147 

0161 

0174 

0188 

0202 

0215 

0229" 

8 

0243 

0256 

0270 

0284 

0297 

0311 

0325 

0338 

0352 

0366 

9 

0379 

0393 

0406 

0420 

0433 

0447 

0461 

0474 

0488 

0501 

320 

50515 

50529 

50542  50556 

50569 

50583 

50596 

50610  50623 

50637 

1 

0651 

0664 

0678 

0691 

0705 

0718 

0732 

0745 

0759 

0772 

2 

0786 

0799 

0813 

0826 

0840 

0853 

0866 

0880 

0893 

0907 

3 

0920 

0934 

0947 

0961 

0974 

0987 

1001 

1014 

1028 

1041 

4 

1055 

1068 

1081 

1095 

1108 

1121 

1135 

1148 

1162 

1175 

5 

1188 

1202 

1215 

1228 

1242 

1255 

1268 

1282 

1295 

1308 

6 

1322 

1335 

1348 

1362 

1375 

1388 

1402 

1415 

1428 

1441 

7 

1455 

1468 

1481 

1495 

1508 

1521 

1534 

1548 

1561 

1574 

8 

1587 

1601 

1614 

1627 

1640 

1654 

1667 

1680 

1693 

1706 

9 

1720 

1733 

1746 

1759 

1772 

1786 

1799 

1812 

1825 

1838 

330 

51851 

51865 

51878 

51891 

51904 

51917 

51930 

51943  51957 

51970 

1 

1983 

1996 

2009 

2022 

2035 

2048 

2061 

2075 

2088 

2101 

2 

2114 

2127 

2140 

2153 

2166 

2179 

2192 

2205 

2218 

2231 

3 

2244 

2257 

2270 

2284 

2297 

2310 

2323 

2336 

2349 

2362 

4 

2375 

2388 

2401 

2414 

2427 

2440 

2453 

2466 

2479 

2492 

5 

2504 

2517 

2530 

2543 

2556 

2569 

2582 

2595 

2608 

2621 

6 

2634 

2647 

2660 

2673 

2686 

2699 

2711 

2724 

2737 

2750 

7 

2763 

2776 

2789 

2802 

2815 

2827 

2840 

2853 

2866 

2879 

8 

2892 

2905 

2917 

2930 

2943 

2956 

2969 

2982 

2994 

3007 

9 

3020 

3033 

3046 

3058 

3071 

3084 

3097 

3110 

3122 

3135 

340 

53148  53161 

53173  53186 

53199 

53212  53224 

53237 

53250 

53263 

1 

3275 

3288 

3301 

3314 

3326 

3339 

3352 

3364 

3377 

3390 

2 

3403 

3415 

3428 

3441 

3453 

3466 

3479 

3491 

3504 

3517 

3 

3529 

3542 

3555 

3567 

3580 

3593 

3605 

3618 

3631 

3643 

4 

3656 

3668 

3681 

3694 

3706 

3719 

3732 

3744 

3757 

3769 

5 

3782 

3794 

3807 

3820 

3832 

3845 

3857 

3870 

3882 

3895 

6 

3908 

3920 

3933 

3945 

3958 

3970 

3983 

3995 

4008 

4020 

7 

4033 

4045 

4058 

4070 

4083 

4095 

4108 

4120 

4133 

4145 

8 

4158 

4170 

4183 

4195 

4208 

4220 

4233 

4245 

4258 

4270 

9 

4283 

429^ 

4307 

4320 

4332 

4345 

4357 

4370 

4382 

4394 

350 

64407 

54419 

54432 

54444 

54456 

54469  54481 

54494  54506 

54518 

496  TABLE  VI.—  LOGARITHMS  OF   NUMBERS. 


N 


23456789 


3 
4 
5 
6 
7 
8 
9 

360 
1 
2 
3 
4 
5 
6 
7 
8 
9 

370 

1 
2 
3 
4 
5 


9 

380 
1 
2 
3 

4 
5 
6 
7 
8 


390 
1 
2 
3 
4 
5 


9 


64407  54419  54432  54444  54456  54469  54481  54494  54506  54518 

4531  4543  4555  4568  4580  4593  4605  4617  4630  4642 

4654  4667  4679  4691  4704  4716  4728  4741  4753  4765 

4777  4790  4802  4814  4827  4839  4851  4864  4876  4888 

4900  4913  4925  4937  4949  41)62  4974  4986  4998  5011 

5023  5035  5047  6060  5072  5084  5096  5108  5121  5133 

5145  5157  5169  6182  5194  6206  .5218  6230  5242  5253 

5267  5279  6291  6303  5315  6328  6340  6352  5364  5376 

6388  5400  5413  5425  6437  6449  6461  5473  5485  5497 

5509  5522  5534  5546  5558  6570  6582  5594  6606  5618 

55630  55642  55654  65666  55678  55691  55703  55715  55727  55739 

5751  5763  5775  5787  6799  5811  6823  5835  5847  5859 

5871  5883  5895  5907  5919  5931  5943  6955  6967  5979 

5991  6003  6015  6027  6038  6050  6062  6074  6086  6098 

6110  6122  6134  6146  6158  6170  618£  6194  6205  6217 

6229  6241  6253  6265  6277  6289  6301  6312  6324  6336 

6348  6360  6372  6384  6396  6407  6419  6431  6443  6455 

6467  6478  6490  6502  6514  6526  6538  6549  6561  6573 

6585  6597  6608  6620  6632  6644  6656  6667  6679  6691 

6703  6714  6726  6738  6750  6761  6773  6785  6797  6808 

56820  56832  56844  56855  56867  56879  56891  56902  56914  56926 

6937  6949  6961  6972  6984  6996  7008  7019  7031  7043 

7054  7066  7078  7089  7101  7113  7124  7136  7148  7169 

7171  7183  7194  7206  7217  7229  7241  7252  7264  7276 

7287  7299  7310  7322  7334  7345  7357  7368  7380  7392 

7403  7415  7426  7438  7449  7461  7473  7484  7496  7507 

7519  7530  7542  7553  7565  7576  7588  7600  7611  7623 

7634  7646  7657  7669  7680  7692  7703  7715  7726  7738 

7749  7761  7772  7784  7795  7807  7818  7830  7841  7852 

7864  7875  7887  .7898  7910  7921  7933  7944  7955  7967 

57978  57990  58001  58013  58024  58035  58047  58058  58070  58081 

8092  8104  8115  8127  8138  8149  8161  8172  8184  8195 

8206  8218  8229  8240  8252  8263  8274  8286  8297  8309 

8320  8331  8343  8354  8365  8377  8388  8399  8410  8422 

8433  8444  8456  8467  8478  8490  8501  8512  8524  8535 

8546  8557  8569  8580  8591  8602  8614  8625  8636  8647 

8659  8670  86.81  8692  8704  8715  8726  8737  8749  8760 

8771  8782  8794  8805  8816  8827  8838  8850  8861  8872 

8883  8894  8906  8917  8928  8939  8950  8961  8973  8984 

8995  9006  9017  9028  9040  9051  9062  9073  9084  9095 

59106  59118  59129  59140  59151  59162  59173  59184  59195  59207 

9218  9229  9240  9251  9262  9273  9284  9295  9306  9318 

9329  9340  9351  9362  9373  9384  9395  9406  9417  9428 

9439  9450  9461  9472  9483  9494  9506  9517  9528  9539 

9550  9561  9572  9583  9594  9605  9616  9627  9638  9649 

9660  9671  9682  9693  9704  9715  9726  9737  9748  9759 

9770  9780  9791  9802  9813  9824  9835  9846  9857  9868 

9879  9890  9901  9912  9923  9934  9945  9956  9966  9977 

9988  9999  60010  60021  60032  60043  60054  60065  60076  60086 

6009760108  0119  0130  0141  0152  0163  0173  0184  0195 


400  1  60206  60217  60228  60239  60249  60260  60271  60282  60293  60304 


TABLE  VI.— LOGARITHMS   OF  NUMBERS.  4Q7 


NO123456789 


3 
4 
5 
6 
7 
8 
9 

410 

1 
2 
3 

4 
5 
6 

7 
8 


420 

1 

2 
3 

4 
5 
6 

7 
8 


430 

1 
2 
3 
4 
5 
6 
7 
8 
9 

440 

1 
2 
3 
4 
5 
6 
7 


450 


60206  60217  60228  60239  60249  602GO  60271  60282  60293  60304 

0314  0325  0336  0347  0358  0369  0379  0390  0401  0412 

0423  0433  0444  0455  0466  0477  0487  0498  0509  0520 

0531  0541  0552  0563  0574  0584  0595  0606  0617  0627 

0638  0649  0660  0670  0681  0692  0703  0713  0724  0733 

0746  0756  0767  0778  0788  0799  0810  0821  0831  0842 

0853  0863  0874  0885  0895  0906  0917  0927  0938  0949 

0959  0970  0981  0991  1002  1013  1023  1034  1045  1055 

1066  1077  1087  1098  1109  1119  1130  1140  1151  1162 

1172  1183  1194  1204  1215  1225  1236  1247  1257  1268 

61278  61289  61300  61310  61321  61331  61342  61352  61363  61374 

1384  1395  1405  1416  1426  1437  1448  1458  1469  1479 

1490  1500  1511  1521  1532  1542  1553  1563  1574  1584 

1595  1606  1616  1627  1637  1648  1658  1669  1679  1690 

1700  1711  1721  1731  1742  1752  1763  1773  1784  1794 

1805  1815  1826  1836  1847  1857  1868  1878  1888  1899 

1909  1920  1930  1941  1951  1962  1972  1982  1993  2003 

2014  2024  2034  2045  2055  2066  2076  2086  2097  2107 

2118  2128  2138  2149  2159  2170  2180  2190  2201  2211 

2221  2232  2242  2252  2263  2273  2284  2294  2304  2315 

62325  62335  62346  62356  62366  62377  62387  62397  62408  62418 

2428  2439  2449  2459  2469  2480  2490  2500  2511  2521 

2531  2542  2552  2562  2572  2583  2593  2603  2613  2624 

2634  2644  2655  2665  2675  2685  2696  2706  2716  2726 

2737  2747  2757  2767  2778  2788  2798  2808  2818  2829 

2839  2849  2859  2870  2880  2890  2900  2910  2921  2931 

2941  2951  2961  2972  2982  2992  3002  3012  3022  3033 

3043  3053  3063  3073  3083  3094  3104  3114  3124  3134 

3144  3155  3165  3175  3185  3195  3205  3215  3225  3236 

3246  3256  3266  3276  3286  3296  3306  3317  3327  3337 

63347  63357  63367  63377  63387  63397  63407  63417  63428  63438 

3448  3458  3468  3478  3488  3498  3508  3518  3528  3538 

3548  3558  3568  3579  3589  3599  3609  3619  3629  3639 

3649  3659  3669  3679  3689  3699  3709  3719  3729  3739 

3749  3759  3769  3779  3789  3799  3809  3819  3829  3839 

3849  3859  3869  3879  3889  3899  3909  3919  3929  3939 

3949  3959  3969  3979  3988  3998  4008  4018  4028  4038 

4048  4058  4068  4078  4088  4098  4108  4118  4128  4137 

4147  4157  4167  4177  4187  4197  4207  4217  4227  4237 

4246  4256  4266  4276  4286  4296  4306  4316  4326  4335 

64345  64355  64365  64375  64385  64395  64404  64414  64424  64434 

4444  4454  4464  4473  4483  4493  4503  4513  4523  4532 

4542  4552  4562  4572  4582  4591  4601  4611  4621  4631 

4640  4650  4660  4670  4680  4689  4699  4709  4719  4729 

4738  4748  4758  4768  4777  4787  4797  4807  4816  4826 

4836  4846  4856  4865  4875  4885  4895  4904  4914  4924 

4933  4943  4953  4963  4972  4982  4002  5002  5011  5021 

5031  5040  5050  5060  6070  5079  5089  5099  5108  5118 

5128  5137  5147  6157  5167  5176  5186  5196  5205  5215 

6225  6234  5244  5254  6263  6273  6283  5292  6302  6312 

65321  65331  65341  65350  65360  65309  65379  65389  65398  65408 


498  TABLE  VI.— LOGARITHMS  OF  NUMBERS. 


0123456789 


450 
1 
2 
3 

4 
5 
6 

7 
8 
9 

460 
1 

2 
3 

4 
5 
6 
7 
8 
9 

470 
1 

2 
3 

4 
5 
6 
7 
8 
9 

480 
1 
2 
3 
4 
5 
6 
7 
8 


490 

1 

2 

.  3 

4 
5 
6 
7 
8 
9 

500 


65321  65331  65341  £5350  65360  65369  65379  65389  65398  65408 

5418  5427  5437  5447  5456  5466  5475  5485  5495  5504 

5514  5523  5533  5543  5552  6562  5571  5581  6591  5600 

5610  5619  5629  5639  5648  5658  5667  5677  5686  5696 

5706  5715  5725  5734  5744  6753  5763  6772  5782  5792 

5801  5811  5820  5830  5839  5849  5858  6868  5877  5887 

5896  6906  5916  5925  5935  5944  5954  5963  5973  5982 

5992  6001  6011  6020  6030  6039  6049  6058  6068  6077 

6087  6096  6106  6115  6124  6134  6143  6153  6162  6172 

6181  6191  6200  621t)  6219  6229  6238  6247  6257  6266 

66276  66285  66295  66304  66314  66323  66332  66342  66351  66361 

6370  6380  6389  6398  6408  6417  6427  6436  6445  6455 

6464  6474  6483  6492  6502  6511  6521  6530  6539  6549 

6558  6567  6577  6586  6596  6605  6614  6624  6633  6642 

6652  6661  6671  6680  6689  6699  6708  6717  6727  6736 

6745  6755  6764  6773  6783  6792  6801  6811  6820  6829 

6839  6848  6857  6867  6876  6885  6894  6904  6913  6922 

6932  6941  6950  6960  6969  6978  6987  6997  7006  7015 

7025  7034  7043  7052  7062  7071  7080  7089  7099  7108 

7117  7127  7136  7145  7154  7164  7173  7182  7191  7201 

67210  67219  67228  67237  67247  67256  67265  67274  67284  67293 

7302  7311  7321  7330  7339  7348  7357  7367  7376  7385 

7394  7403  7413  7422  7431  7440  7449  7459  7468  7477 

7486  7495  7504  7514  7523  7532  7541  7550  7560  7569 

7578  7587  7596  7605  7614  7624  7633  7642  7651  7660 

7669  7679  7688  7697  7706  7715  7724  7733  7742  7752 

7761  7770  7779  7788  7797  7806  7815  7825  7834  7843 

7852  7861  7870  7879  7888  7897  7906  7916  7925  7934 

7943  7952  7961  7970  7979  7988  7997  8006  8015  8024 

8034  8043  8052  8061  8070  8079  8088  8097  8106  8115 

68124  68133  68142  68151  68160  68169  68178  68187  68196  68205 

8215  8224  8233  8242  8251  8260  8269  8278  8287  8296 

8305  8314  8323  8332  8341  8350  8359  8368  8377  8386 

8395  8404  8413  8422  8431  8440  8449  8458  8467  8476 

8485  8494  8502  8511  8520  8529  8538  8547  8556  8565 

8574  8583  8592  8601  8610  8619  8628  8637  8646  8655 

8664  8673  8681  8690  8699  8708  8717  8726  8735  8744 

8753  8762  8771  8780  8789  8797  8806  8815  8824  8833 

8842  8851  8860  8869  8878  8886  8895  8904  8913  8922 

8931  8940  8949  8958  8966  8975  8984  8993  9002  9011 

69020  69028  69037  69046  69055  69064  69073  69082  69090  69099 

9108  9117  9126  9135  9144  9152  9161  9170  9179  9188 

9197  9205  9214  9223  9232  9241  9249  9258  9267  9276 

9285  9294  9302  9311  9320  9329  9338  9346  9355  9364 

9373  9381  9390  9399  9408  9417  9425  9434  9443  9452 

9461  9469  9478  9487  9496  9504  9513  9522  9531  9539 

9548  9557  9566  9574  9583  9592  9601  9609  9618  9627 

9636  9644  9653  9662  9671  9679  9688  9697  9705  9714 

9723  9732  9740  9749  9758  9767  9775  9784  9793  9801 

9810  9819  9827  9836  9845  9854  9862  9871  9880  9888 

69897  69906  69914  69923  69932  69940  69949  69958  69966  69975 


TABLE  VI.— LOGARITHMS  OF  NUMBERS.     499 


N 

600^ 

1 
2 
3 
4 
5 
6 
7 


510 

1 

2 
3 
4 
5 
6 
7 
8 


520 
1 

2 
3 

4 
5 
6 

7 


530 

1 

2 
3 
4 
5 
6 
7 
8 
9 

540 

1 

2 
3 

4 
5 
6 

7 


550 


5678 


(59897  69906  69914  69923  69932  6994Q  69949  69958  69966  69975 

9984  9992  70001  70010  70018  70027  70036  70044  70053  70062 

70070  70079  0088  0096  0105  0114  0122  0131  0140  0148 

0157  0165  0174  0183  0191  0200  0209  0217  0226  0234 

0243  0252  0260  0269  0278  0286  0295  0303  0312  0321 

0329  0338  0346  0355  0364  0372  0381  0389  0398  0406 

0415  0424  0432  •  0441  0449  0458  0467  0475  0484  0492 

0501  0509  0518  0526  0535  0544  0552  0561  0569  0578 

0586  0595  0603  0612  0621  0629  0638  0646  0655  0663 

0672  0680  0689  0697  0706  0714  0723  0731  0740  0749 

70757  70766  70774  70783  70791  70800  70808  70817  70825  70834 

0842  0851  0859  0868  0876  0885  0893  0902  0910  0919 

0927  0935  0944  0952  0961  0969  0978  0986  0995  1003 

1012  1020  1029  1037  1046  1054  1063  1071  1079  1088 

1096  1105  1113  1122  1130  1139  1147  1155  1164  1172 

1181  1189  1198  1206  1214  1223  1231  1240  1248  1257 

1265  1273  1282  1290  1299  1307  1315  1324  1332  1341 

1349  1357  1366  1374  1383  1391  1399  1408  1416  1425 

1433  1441  1450  1458  1466  1475  1483  1492  1500  1508 

1517  1525.  1533  1542  1550  1559  1567  1575  1584*  1592 

71600  71609  71617  71625  71634  71642  71650  71659  71667  71675 

1684  1692  1700  1709  1717  1725  1734  1742  1750  1759 

1767  1775  1784  1792  1800  1809  1817  1825  1834  1842 

1850  1858  1867  1875  1883  1892  1900  1908  1917  1925 

1933  1941  1950  1958  1966  1975  1983  1991  1999  2008 

2016  2024  2032  2041  2049  2057  2066  2074  2082  2090 

2099  2107  2115  2123  2132  2140  2148  2156  2165  2173 

2181  2189  2198  2206  2214  2222  2230  2239  2247  2255 

2263  2272  2280  2288  2296  2304  2313  2321  2329  2337 

2346  2354  2362  2370  2378  2387  2395  2403  2411  2419 

72428  72436  72444  72452  72460  72469  72477  72485  72493  72501 

2509  2518  2526  2534  2542  2550  2558  2567  2575  2583 

2591  2599  2607  2616  2624  2632  2640  2648  2656  2665 

2673  2681  2689  2697  2705  2713  2722  2730  2738  2746 

2754  2762  2770  2779  2787  2795  2803  2811  2819  2827 

2835  2843  2852  2860  2868  2876  2884  2892  2900  2908 

2916  2925  2933  2941  2949  2957  2965  2973  2981  2989 

2997  3006  3014  3022  3030  3038  3046  3054  3062  3070 

3078  3086  3094  3102  3111  3119  3127  3135  3143  3151 

3159  3167  3175  3183  3191  3199  3207  3215  3223  3231 

73239  73247  73255  73263  73272  73280  73288  73296  73304  73312 

3320  3328  3336  3344  3352  3360  3368  3376  3384  3392 

3400  3408  3416  3424  3432  3440  3448  3456  3464  3472 

3480  3488  3496  3504  3512  3520  3528  3536  3544  3552 

3560  3568  3576  3584  3592  3600  3608  3616  3624  3632 

3640  3648  3656  3664  3672  3679  3687  3695  3703  3711 

3719  3727  3735  3743  3751  3759  3767  3775  3783  3791 

3799  3807  3815  3823  3830  3838  3846  3854  3862  3870 

3878  3886  3894  3902  3910  3918  3926  3933  3941  3949 

3957  3965  3973  3981  3989  3997  4005  4013  4020  4028 

74036  74044  74052  74060  74068  74076  74084  74092  74099  74107 


500 


TABLE  VI.— LOGARITHMS  OF   NUMBERS. 


N 

o 

1 

2 

3 

4 

5 

6 

7 

8 

9 

550 

74036 

74044 

74052 

74060 

74068  74076 

74084 

74092 

74099 

74107 

1 

4115 

4123 

4131 

4139 

4147 

4155 

4162 

4170 

4178 

4186 

2 

4194 

4202 

4210 

4218 

4225 

4233 

4241 

4249 

4257 

4265 

3 

4273 

4280 

4288 

4296 

4304 

4312 

4320 

4327 

4335 

4343 

4 

4351 

4359 

4367 

4374 

4382 

4390 

4398 

4406 

4414 

4421 

5 

4429 

4437 

4445 

4453 

4461 

4468 

4476 

4484 

4492 

4500 

6 

4507 

4515 

4523 

4531 

4539 

4547' 

4554 

4562 

4570 

4578 

7 

4586 

4593 

4601 

4609 

4617 

4624 

4632 

4640 

4648 

4656 

8 

4663 

4671 

4679 

4687 

4(595 

4702 

4710 

4718 

4726 

4733 

9 

4741 

4749 

4757 

4764 

4772 

4780 

4788 

4796 

4803 

4811 

560 

74819  74827 

74834  74842 

74850 

74858 

74865 

74873 

74881 

74889 

1 

4896 

4904 

4912 

4920 

4927 

4935 

4943 

4950 

4958 

4966 

2 

4974 

4981 

4989 

4997 

5005 

5012 

5020 

5028 

5035 

5043 

3 

5051 

5059 

5066 

6074 

5082 

5089 

5097 

5105 

5113 

5120 

4 

5128 

5136 

5143 

5151 

5159 

6166 

5174 

6182 

5189 

5197 

5 

5205 

5213 

5220 

5228 

5236 

6243 

5251 

5259 

5266 

5274 

6 

5282 

5289 

5297 

5305 

5312 

5320 

6328 

6335 

5343 

5351 

7 

5358 

5366 

5374 

5381 

5389 

5397 

6404 

6412 

6420 

5427 

8 

.5435 

5442 

5450 

6458 

5465 

6473 

5481 

5488 

5496 

5504 

9 

5511 

5519 

5526 

5534 

5542 

5549 

5557 

.5565 

5572 

5580 

570 

75587 

75595  75603 

75610 

75618 

75626 

75633 

75641 

75648 

75656 

1 

5664 

5671 

5679 

5686 

5694 

5702 

5709 

5717 

5724 

5732 

2 

5740 

5747 

5755 

5762 

5770 

5778 

5785 

5793 

5800 

5808 

3 

5815 

5823 

5831 

6838 

5846 

5853 

5861 

5868 

5876 

5884 

4 

5891 

5899 

5906 

5914 

5921 

5929 

5937 

5944 

5952 

5959 

5 

5967 

5974 

5982 

5989 

5997 

6005 

6012 

6020 

6027 

6035 

6 

6042 

6050 

6057 

606^ 

6072 

6080 

6087 

6095 

6103 

6110 

7 

6118 

6125 

6133 

6140 

6148 

6155 

6163 

6170 

6178 

6185 

8 

6193 

6200 

6208 

6215 

6223 

6230 

6238 

6245 

6253 

6260 

9 

6268 

6275 

6283 

6290 

6298 

6305 

6313 

6320 

6328 

6335 

580 

76343 

76350  76358 

76365  76373 

76380 

76388  76395 

76403 

76410 

1 

6418 

6425 

6433 

6440 

6448 

6455 

6462 

6470 

6477 

6485 

2 

6492 

6500 

6507 

6515 

6522 

6530 

6537 

6545 

6552 

6559 

3 

6567 

6574 

6582 

6589 

6597" 

6604 

6612 

6619 

6626 

6634 

4 

6641 

6649 

6656 

6664 

6671 

6678 

6686 

6693 

6701 

6708 

5 

6716 

6723 

6730 

6738 

6745 

6753 

6760 

6768 

6775 

6782 

6 

6790 

6797 

6805 

6812 

6819 

6827 

6834 

6842 

6849 

6856 

7 

6864 

6871 

6879 

6886 

6893 

6901 

6908 

6916 

6923 

6930 

8 

6938 

6945 

6953 

6960 

6967 

6975 

6982 

6989 

6997 

7004 

9 

7012 

7019 

7026 

7034 

7041 

7048 

7056 

7063 

7070 

7078 

590 

77085 

77093  77100 

77107 

77115 

77122 

77129 

77137 

77144 

77151 

1 

7159 

7166 

7173 

7181 

7188 

7195 

7203 

7210 

7217 

7225 

2 

7232 

7240 

7247 

7254 

7262 

7269 

7276 

7283 

7291 

7298 

3 

7305 

7313 

7320 

7327 

7335 

7342 

7349 

7357 

7364 

7371 

4 

7379 

7386 

7393 

7401 

7408 

7415 

7422 

7430 

7437 

7444 

5 

7452 

7459 

7466 

7474 

7481 

7488 

7495 

7503 

7510 

7517 

6 

7525 

7532 

7539 

7546 

7554 

7561 

7568 

7576 

7583 

7590 

7 

7597 

7605 

7612 

7619 

7627 

7634 

7641 

7648 

7656 

7663 

8 

7670 

7677 

7685 

7692 

7699 

7706 

7714 

7721 

7728 

7735 

9 

7743 

7750 

7757 

7764 

7772 

7779 

7786 

7793 

7801 

7808 

600 

77815 

77822 

77830 

77837 

77844 

77851 

77859 

77866 

77873 

77880 

TABLE  VI.— LOGARITHMS  OP  NUMBERS.  5Q1 


23456789 


600 
1 

2 
3 

4 


7 
8 
9 

610 
1 

2 
3 
4 
5 
6 
7 


620 
1 
2 

3 

4 
5 
6 

7 
8 


630 
1 

2 
3 
4 
5 
6 
7 
8 
9 

640 

1 

2 
3 

4 
5 
S 

7 
8 


650 


77815  77822  77830  77837  77844  77851  77859  77866  77873  77880 

7887  7895  7902  7909  7916  7924  7931  7938  7945  7952 

7960  7967  7974  7981  7988  7996  8003  8010  8017  8025, 

8032  8039  8046  8053  8061  8068  8075  8082  8089  8097 

8104  8111  8118  8125  8132  8140  8147  8154  8161  8168 

8176  8183  8190  8197  8204  8211  8219  8226  8233  8240 

8247  8254  8262  8269  8276  8283  8290  8297  8305  8312 

8319  8326  8333  8340  8347  8355  8362  8369  8376  8383 

8390  8398  8405  8412  8419  8426  8433  8440  8447  8455 

8462  8469  8476  8483  8490  8497  8504  8512  8519  8526 

78533  78540  78547  78554  78561  78569  78576  78583  78590  78597 

8604  8611  8618  8625  8633  8640  8647  8654  8661  8668 

8675  8682  8689  8696  8704  8711  8718  8725  8732  8739 

8746  8753  8760  8767  8774  8781  8789  8796  8803  8810 

8817  8824  8831  8838  8845  8852  8859  8866  8873  8880 

8888  8895  8902  8909  8916  8923  8930  8937  8944  8951 

8958  8965  8972  8979  8986  8993  9000  9007  9014  9021 

9029  9036  9043  9050  9057  9064  9071  9078  9085  9092 

9099  9106  9113  9120  9127  9134  9141  9148  9165  9162 

9169  9176  9183  9190  9197  9204  9211  9218  9225  9232 

79239  79246  79253  79260  79267  79274  79281  79288  79295  79302 

9-J09  9316  9323  9330  9337  9344  9351  9358  9365  9372 

9379  9386  9393  9400  9407  9414  9421  9428  9435  9442 

9449  9456  9463  9470  9477  9484  9491  9498  9505  9511 

9518  9525  9532  9539  9546  9553  9560  9567  9574  9581 

9588  9595  9602  9609  9616  9623  9630  9637  9644  9650 

9657  9664  9671  9678  9685  9692  9699  9706  9713  9720 

9727  9734  9741  9748  9754  9761  9768  9775  9782  9789 

9796  9803  9810  9817  9824  9831  9837  9844  9851  9858 

9865  9872  9879  9886  9893  9900  9906  9913  9920  9927 

79934  79941  79948  79955  79962  79969  79975  79982  79989  79996 

80003  80010  80017  80024  80030  80037  80044  80051  80058  80065 

0072  0079  0085  0092  0099  0106  0113  0120  0127  0134 

0140  0147  0154  0161  0168  0175  0182  0188  0195  0202 

0209  0216  0223  0229  0236  0243  0250  0257  0264  0271 

0277  0284  0291  0298  0305  0312  0318  0325  0332  0339 

0346  0353  0359  0366  0373  0380  0387  0393  0400  0407 

0414  0421  0428  0434  0441  0448  0455  0462  0468  0475 

0482  0489  0496  0502  0509  0516  0523  0530  0536  0543 

0550  0557  '0564  0570  0577  0584  0591  0598  0604  0611 

80618  80625  80632  80638  80645  80652  80659  80665  80672  80679 

0686  0693  0699  0706  0713  0720  0726  0733  0740  0747 

0754  0760  0767  0774  0781  0787  0794  0801  0808  0814 

0821  0828  0835  0841  0848  0855  0862  0868  0875  0882 

0889  0895  0902  0909  0916  0922  0929  0936  0943  0949 

0956  0963  0969  0976  0983  0990  0996  1003  1010  1017 

1023  1030  1037  1043  1050  1057  1064  1070  1077  1084 

1090  1097  1104  1111  1117  1124  1131  1137  1144  1151 

1158  1164  1171  1178  1184  1191  1198  1204  1211  1218 

1224  1231  1238  1245  1251  1258  1265  1271  1278  1285 

81291  81298  81305  81311  81318  81325  81331  81338  81345  81351 


502  TABLE  VI.— LOGARITHMS  OP  NUMBERS. 


3456789 


650 

1 
2 
3 
4 
5 
6 
7 
8 
9 

660 
1 
2 
3 
4 
5 
6 
7 
8 


670 

1 
2 
3 
4 
5 
6 
7 
8 
9 

680 

1 
2 
3 
4 
5 
6 
7 
8 
9 

690 

1 
2 
3 
4 
5 
6 
7 
8 
9 

700 


81291  81298  81305  81311  81318  81325  81331  81338  81345  81351 

1358  1365  1371  1378  1385  1391  1398  1405  1411  1418 

1425  1431  1438  1445  1451  1458  1465  1471  1478  1485 

1491  1498  1505  1511  1518  1525  1531  1538  1544  1551 

1558  1564  1571  1578  1584  1591  1598  1604  1611  1617 

1624  1631  1637  1644  1651  1657  1664  1671  1677  1684 

1690  1697  1704  1710  1717  1723  1730  1737  1743  1750 

1757  1763  1770  1776  1783  1790  1796  1803  1809  1816 

1823  1829  1836  1842  1849  1856  1862  1869  1875  1882 

1889  1895  1902  1908  1915  1921  1928  1935  1941  1948 

81954  81961  81968  81974  81981  81987  81994  82000  82007  82014 

2020  2027  2033  2040  2046  2053  2060  2066  2073  2079 

2086  2092  2099  2105  2112  2119  2125  2132  2138  2145. 

2151  2158  2164  2171  2178  2184  2191  2197  2204  2210 

2217  2223  2230  2236  2243  2249  2256  2263  2269  2276 

2282  2289  2295  2302  2308  2315  2321  2328  2334  2341 

2347  2354  2360  2367  2373  2380  2387  2393  2400  2406 

2413  2419  2426  2432  2439  2445  2452  2458  2465.  2471 

2478  2484  2491  2497  2504  2510  2517  2523  2530  2536 

2543  2549  2556  2562  2569  2575  2582  2588  2595  2601 

82607  82614  82620  82627  82633  82640  82646  82653  82659  82666 

2672  2679  2685  2692  2698  2705  2711  2718  2724  2730 

2737  2743  2750  2756  2763  2769  2776  2782  2789  2795 

2802  2808  2814  2821  2827  2834  2840  2847  2853  2860 

2866  2872  2879  2885  2892  2898  2905  2911  2918  2924 

2930  2937  2943  2950  2956  2963  2969  2975  2982  2988 

2995  3001  3008  3014  3020  3027  3033  3040  3046  3052 

3059  3065  3072  3078  3085  3091  3097  3104  3110  3117 

3123  3129  3136  3142  3149  3155  3161  3168  3174  3181 

3187  3193  3200  3206  3213  3219  3225  3232  3238  3245 

83251  83257  €3264  83270  83276  83283  83289  83296  83302  83308 

3315  3321  3327  3334  3340  3347  3353  3359  3366  3372 

3378  3385  3391  3398  3404  3410  3417  3423  3429  3436 

3442  3448  3455  3461  3467  3474  3480  3487  3493  3499 

3506  3512  3518  3525  3531  3537  3544  3550  3556  3563 

3569  3575  3582  3588  3594  3601  3607  3613  3620  3626 

3632  3639  3645  3651  3658  3664  3670  3677  3683  3689 

3696  3702  3708  3715  3721  3727  3734  3740  3746  3753 

3759  3765  3771  3778  3784  3790  3797  3803  3809  3816 

3822  3828  3835  3841  3847  3853  3860  3866  3872  3879 

83885  83891  83897  83904  83910  83916  83923  83929  83935  83942 

3948  3954  3960  3967  3973  3979  3985  3992  3998  4004 

4011  4017  4023  4029  4036  4042  4048  4055  4061  4067 

4073  4080  4086  4092  4098  4105  4111  4117  4123  4130 

4136  4142  4148  4155  4161  4167  4173  4180  4186  4192 

4198  4205  4211  4217  4223  4230  4236  4242  4248  4255 

4261  4267  4273  4280  4286  4292  4298  4305  4311  4317 

4323  4330  4336  4342  4348  4354  4361  4367  4373  43^9 

4386  4392  4398  4404  4410  4417  4423  4429  4435  4442 

4448  4454  4460  4466  4473  4479  4485  4491  4497  4504 

84510  84516  84522  84528  84535  84541  84547  84553  84559  84566 


TABLE  VI.— LOGARITHMS  OF   NUMBERS.  503 


700 

1 
2 
3 
4 
5 
6 
7 
8 


710 

1 

2 
3 

4 
5 
6 

7 
8 
9 

720 

1 

2 
3 

4 
5 
6 

7 
8 


730 

1 

2 

3 
4 
5 
6 

7 
8 
9 

740 
1 

2 
3 

4 
5 
6 

7 


750 


23456789 


84510  84516  84522  84528  84535  84541  84547  84553  84559  84566 

-1">72  4578  4584  4590  4597  4603  4609  4615  4621  4628 

4634  4640  4646  4(552  4658  4665  4671  4677  4683  4689 

4696  4702  4708  4714  4720  4726  4733  4739  4745  4751 

4757  4763  4770  4776  4782  4788  4794  4800  4807  4813 

4819  4825  4831  4837  4844  4850  4856  4862  4868  4874 

4880  4887  4893  4899  4905  4911  4917  4924  4930  4936 

4942  4948  4954  4960  4967  4973  4979  4983  4991  4997 

5003  5009  5016  5022  6028  6034  6040  6046  6052  6058 

6065  5071  6077  6083  6089  6095  6101  6107  6114  6120 

85126  85132  85138  85144  85150  85156  85163  85169  85175  85181 

5187  5193  5199  5205  5211  6217  6224  6230  6236  6242 

5248  5254  5260  6266  6272  6278  6285  5291  5297  5303 

5309  6315  5321  5327  5333  6339  6345  5352  5358  6364 

5370  6376  5382  5388  5394  5400  6406  5412  6418  6425 

5431  6437  6443  6449  5455  5401  A4IJ7  5473  6479  5485 

5491  6497  5503  6509  5516  5522  6528  5534  5540  5546 

5552  6558  6564  5570  5576  6582  5588  6594  5600  5606 

5612  5618  5625  5631  6637  5643  6649  6655  5661  5667 

5673  6679  6685  5691  6697  6703  6709  6715  6721  6727 

85733  85739  85745  85751  85757  85763  85769  85775  85781  85788 

5794  5800  6806  6812  6818  6824  5830  6836  6842  5848 

5854  5860  6866  6872  5878  6884  5890  6896  6902  6908 

5914  6920  5926  6932  5938  6944  6950  6956  6962  6968 

6974  5980  5986  6992  5998  6004  6010  6016  6022  6028 

6034  6040  6046  6052  6058  6064  6070  6076  6082  6088 

6094  6100  6106  6112  6118  6124  6130  6136  6141  6147 

6153  6159  6165  6171  6177  6183  6189  6195  6201  6207 

6213  6219  6225  6231  6237  6243  6249  6255  6261  6267 

6273  6279  6283  6291  6297  6303  6308  6314  6320  6326 

86332  86338  86344  86350  86356  86362  86368  86374  86380  86386 

6392  6398  6404  6410  6415  6421  6427  6433  6439  6445 

6451  6457  6463  6469  6475  6481  6487  6493  6499  6504 

6510  6516  6522  6528  6534  6540  6546  6552  6558  6564 

6570  6576  6581  6587  6593  6599  6605  6611  6617  6623 

6629  6635  6641  6646  6652  6658  6664  6670  6676  6682 

6688  6694  6700  6705  6711  6717  6723  6729  6735  6741 

6747  6753  6759  6764  6770  6776  6782  6788  6794  6800 

6806  6812  6817  6823  6829  6835  6841  6847  6853  6869 

6864  6870  6876  6882  6888  6894  6900  6906  6911  6917 

86923  86929  86935  86941  86947  86953  86958  86964  86970  86976 

6982  6988  6994  6999  7005  7011  7017  7023  7029  7035 

7040  7046  7052  7058  7064  7070  7075  7081  7087  7093 

7099  7105  7111  7116  7122  7128  7134  7140  7146  7151 

7157  7163  7169  7175  7181  7186  7192  7198  7204  7210 

7262  7268 

7315  7320  7326 

7332  7338  7344  7349  7355  7361  7367  7373  7379  7384 

7390  7396  7402  7408  7413  7419  7425  7431  7437  7442 

7448  7454  7460  7466  7471  7477  7483  7489  7495  7600 

87506  87512  87518  87523  87529  87535  87541  87547  87552  87658 


7216  7221  7227  7233  7239  7245  7251  7256 
7274  7280  7286  7291  7297  780.T"  7309  7315 


504 


TABLE  VI.— LOGARITHMS  OF  NUMBERS. 


750 
1 

2 
3 

4 
5 
6 

7 


760 
1 

2 
3 
4 
5 


770 

1 

2 
3 
4 
5 
6 

r 

8 
9 

780 
1 
2 
3 
4 
5 
6 
7 
8 
9 

790 

1 
2 
3 

4 


7 
8 
9 

800 


O 


8   9 


87506 
7564 
7622 
7679 
7737 
7795 
7852 
7910 
7967 
8024 

88081 
8138 
8195 
8252 
8309 
8366 
8423 
8480 
8536 
8593 

88649 
8705 
8762 
8818 
8874 
8930 
8986 
9042 
9098 
9154 


87512 
7570 
7628 
7685 
7743 
7800 
7858 
7915 
7973 
8030 

88087 
8144 
8201 
8258 
8315 
8372 
8429 
8485 
8542 
8598 

88655 
8711 
8767 
8824 
8880 
8936 
8992 
9048 
9104 
9159 


89209  89215 

9265  9271 

9321  9326 

9376  9382 

9432  9437 

9487  9492 

9542  9548 

9597  9603 

9653  9658 

9708  9713 


87518 
7576 
7633 
7691 
7749 
7806 
7864 
7921 
7978 
8036 

88093 
8150 
8207 
8264 
8321 
8377 
8434 
8491 
8547 
8604 

88660 
8717 
8773 
8829 
8885 
8941 
8997 
9053 
9109 
9165 

89221 
9276 
9332 
9387 
9443 
9498 
9553 
9609 
9664 
9719 


87523 
7581 


7697 
7754 
7812 
7869 
7927 
7984 
8041 

88098 
8156 
8213 
8270 
8326 
8383 
8440 
8497 
8553 
8610 

88666 
8722 
8779 
8835 
8891 
8947 
9003 
9059 
9115 
9170 

89226 
'  9282 
9337 
9393 
9448 
9504 
9559 
9614 
9669 
9724 


87529  87535 

7587  7593 

7645  7651 

7703  7708 

7760  7766 

7818  7823 

7875  7881 

7933  7938 

7990  7996 

8047  8053 


88104 
8161 
8218 
8275 
8332 
8389 
8446 
8502 
8559 
8615 

88672 
8728 
8784 
8840 
8897 
8953 
9009 
9064 
9120 
9176 

89232 
9287 
9343 


9454 
9509 
9564 
9620 
9675 
9730 


88110 
8167 
8224 
8281 
8338 
8395 
8451 
8508 
8564 
8621 

88677 
8734 
8790 
8846 
8902 
8958 
9014 
9070 
9126 
9182 

89237 
9293 
9348 
9404 
9459 
9515 
9570 
9625 
9680 
9735 


87541 
7599 
7656 
7714 
7772 
7829 
7887 
7944 
8001 
8058 

88116 
8173 
8230 
8287 
8343 
8400 
8457 
8513 
8570 
8627 

88683 
8739 
8795 
8852 
8908 
8964 
9020 
9076 
9131 
9187 

89243 
9298 
9354 
9409 
9465 
9520 
9575 
9631 
9686 
9741 


87547 
7604 
7662 
7720 
7777 
7835 
7892 
7950 
8007 
8064 

88121 
8178 
8235 
8292 
8349 
8406 
8463 
8519 
8576 
8632 


87552 
7610 
7668 
7726 
7783 
7841 
7898 
7955 
8013 
8070 

88127 
8184 
8241 
8298 
8355 
8412 
8468 
8525 
8581 
8638 


89763  89768  89774  89779 
9818  9823  9829  9834 
9873  9878  9883  9889 
9927  9933  9938  9944 
9982  9988  9993  9998 

90037  90042  90048  90053 
0091  0097  0102  0108 
0146  0151  0157  0162 
0200  0206  0211  0217 
0255  0260  0266  0271 

90309  90314  90320  90325 


89785  89790  89796 
9840  9845  9851 
9894  9900  9905 
9949  9955  9960 

90004  90009  90015 
0059  0064  0069 
0113  0119  0124 
0168  0173  0179 
0222  0227  0233 
0276  0282  0287 

90331  90336  90342 


88689  88694 

8745  8750 

8801  8807 

8857  8863 

8913  8919 

8969  8975 

9025  9031 

9081  9087 

9137  9143 

9193  9198 

89248  89254 

9304  9310 

9360  9365 

9415  9421 

9470  9476 

9526  9531 

9581  9586 

9636  9642 

9691  9697 

9746  9752 

89801  89807 

9856  9862 

9911  9916 

9966  9971 

90020  90026 

0075  0080 

0129  0135 

0184  0189 

0238  0244 

0293  0298 


87558 
7616 
7674 
7731 
7789 
7846 
7904 
7961 
8018 
8076 

88133 
8190 
8247 
8304 
8360 
8417 
8474 
8530 
8587 
8643 

88700 
8756 
8812 
8868 
8925 
8981 
9037 
9092 
9148 
9204 

89260 
9315 
9371 
9426 
9481 
9537 
9592 
9647 
9702 
9757 

89812 
9867 
9922 
9977 

90031 
0086 
0140 
0195 
024^ 
0304 


90347  90352  90:558 


TABLE  VI.— LOGARITHMS  OF   NUMBERS.  505 


N012345678 


800 
1 
2 
3 
4 
5 
6 
7 


810 

1 
2 
3 
4 
5 


820 

1 
2 
3 
4 
5 


840 
1 
2 
3 
4 
5 
6 
7 
8 
9 

850 


90309  90314  90320  90325  90331  90336  90342  90347  90352  90358 

0363  0369  0374  0380  0385  0390  0396  0401  0407  0412 

0417  0423  0428  0434  0439  0445  0450  0455  0461  0466 

0472  0477  0482  0488  0493  0499  0504  0509  0515  0520 

0526  0531  0536  0542  0547  0553  0558  0563  0569  0674 

0580  0585  0590  0596  0601  0607  0612  0617  0623  0628 

0634  0639  0644  0650  0655  0660  0666  0671  0677  0682 

0687  0693  0698  0703  0709  0714  0720  0725  0730  0736 

0741  0747  0752  0757  0763  0768  0773  0779  0784  0789 

079^  0800  0806  0811  0816  0822  0827  0832  0838  0843 

90849  90854  90859  90865  90870  90875  90881  90886  90891  90897 

0902  0907  0913  0918  0924  0929  0934  0940  0945  0950 

0956  0961  0966  0972  0977  0982  0988  0993  0998  1004 

1009  1014  1020  1025  1030  1036  1041  1046  1052  1057 

1062  1068  1073  1078  1084  1089  1094  1100  1105  1110 

1116  1121  1126  1132  1137  1142  1148  1153  1158  1164 

1169  1174  1180  1185  1190  1196  1201  1206  1212  1217 

1222  1228  1233  1238  1243  1249  1254  1259  1265  1270 

1275  1281  1286  1291  1297  1302  1307  1312  1318  1323 

1328  1334  1339  1344  1350  1355  1360  1365  1371  1376 

91381  91387  91392  91397  91403  91408  91413  91418  91424  91429 

1434  1440  1445  1450  1455  1461  1466  1471  1477  1482 

1487  1492  1498  1503  1508  1514  1519  1524  1529  1535 

1540  1545  1551  1556  1561  1566  1572  1577  1582  1587 

1593  1598  1603  1609  1614  1619  1624  1630  1635  1640 

1645  1651  1656  1661  1666  1672  1677  1682  1687  1693 

1698  1703  1709  1714  1719  1724  1730  1735  1740  1745 

1751  1756  1761  1766  1772  1777  1782  1787  1793  1798 

1803  1808  1814  1819  1824  1829  1834  1840  1845  1850 

1855  1861  1866  1871  1876  1882  1887  1892  1897  1903 

91908  91913  91918  91924  91929  91934  91939  91944  91950  91955 

1960  1965  1971  1976  1981  1986  1991  1997  2002  2007 

2012  2018  2023  2028  2033  2038  2044  2049  2054  2059 

2065  2070  2075  2080  2085  2091  2096  2101  2106  2111 

2117  2122  2127  2132  2137  2143  2148  2153  2158  2163 

2169  2174  2179  2184  2189  2195  2200  2205  2210  2215 

2221  2226  2231  2236  2241  2247  2252  2257  2262  2267 

2273  2278  2283  2288  2293  2298  2304  2309  2314  2319 

2324  2330  2335  2340  2345  2350  2355  2361  2366  2371 

2376  2381  2387  2392  2397  2402  2407  2412  2418  2423 

92428  92433  92438  92443  92449  92454  92459  92464  92469  92474 

2480  2485  2490  2495  2500  2505  2511  2516  2521  2526 

2531  2536  2542  2547  2552  2557  2562  2567  2572  2578 

2583  2588  2593  2598  2603  2609  2614  2619  2624  2629 

2634  2639  2645  2650  2655  2660  2665  2670  2675  2681 

2686  2691  2696  2701  2706  2711  2716  2722  2727  2732 

2737  2742  2747  2752  2758  2763  2768  2773  2778  2783 

2788  2793  2799  2804  2809  2814  2819  2824  2829  2834 

2840  2845  2850  2855  2860  2865  2870  2875  2881  2886 

2891  2896  2901  2906  2911  2916  2921  2927  2932  2937 

92942  92947  92952  92957  92962  92967  92973  92978  92983  92988 


506  TABLE  VI.— LOGARITHMS  OF  NUMBERS. 


O12345678 


850 
1 

2 
3 

4 
5 
6 
7 
8 
9 

860 
1 


870 
1 


880 
1 
2 
3 
4 
5 
6 
7 
8 
9 

890 
1 

2 
3 

4 
5 
6 
7 
8 
9 

900 


92942  92947  92952  92957  92962  92967  92973  92978  92983  92988 

2993  2998  3003  3008  3013  3018  3024  3029  3034  3039 

3044  3049  3054  3059  3064  3069  3075  3080  3085  3090 

3095  3100  3105  3110  3115  3120  3125  3131  3136  3141 

3146  3151  3156  3161  3166  3171  3176  3181  3186  3192 

3197  3202  3207  3212  3217  3222  3227  3232  3237  3242 

3247  3252  3258  3263  3268  3273  3278  3283  3288  3293 

3298  3303  3308  3313  3318  3323  3328  3334  3339  3344 

3349  3354  3359  3364  3369  3374  3379  3384  3389  3394 

3399  3404  3409  3414  3420  342*  3430  343£  3440  3445 

93450  93455  93460  93465  93470  93475  93480  93485  93490  93495 

3500  3505  3510  3515  3520  3526  3531  3536  3541  3546 

3551  3556  3561  3566  3571  3576  3581  3586  3591  3596 

3601  3606  3611  3616  3621  3626  3631  3636  3641  3646 

3651  3656  3661  3666  3671  3676  3682  3687  3692  3697 

3702  3707  3712  3717  3722  3727  3732  3737  3742  3747 

3752  3757  3762  3767  3772  3777  3782  3787  3792  3797 

3802  3807  3812  3817  3822  3827  3832  3837  3842  3847 

3852  3857  3862  3867  3872  3877  3882  3887  3892  3897 

3902  3907  3912  3917  3922  3927  3932  3937  3942  3947 

93952  93957  93962  93967  93972  93977  93982  93987  93992  93997 

4002  4007  4012  4017  4022  4027  4032  4037  4042  4047 

4052  4057  4062  4067  4072  4077  4082  4086  4091  4096 

4101  4106  4111  4116  4121  4126  4131  4136  4141  4146 

4151  4156  4161  4166  4171  4176  4181  4186  4191  4196 

4201  4206  4211  4216  4221  4226  4231  4236  4240  4245 

4250  4255  4260  4265  4270  4275  4280  4285  4290  4295 

4300  4305  4310  4315  4320  4325  4330  4335  4340  4345 

4349  4354  4359  4364  4369  4374  4379  4384  4389  4394 

4399  4404  4409  4414  4419  4424  4429  4433  4438  4443 

94448  94453  94458  94463  94468  94473  94478  94483  94488  94493 

4498  4503  4507  4512  4517  4522  4527  4532  4537  4542 

4547  4552  4557  4562  4567  4571  4576  4581  4586  4591 

4596  4601  4606  4611  4616  4621  4626  4630  4635  4640 

4645  4650  4655  4660  4665  4670  4675  4680  4685  4689 

4694  4699  4704  4709  4714  4719  4724  4729  4734  4738 

4743  4748  4753  4758  4763  4768  4773  4778  4783  4787 

4792  4797  4802  4807  4812  4817  4822  4827  4832  4836 

4841  4846  4851  4856  4861  4866  4871  4876  4880  4885 

4890  4895  4900  4905  4910  4915  4919  4924  4929  4934 

94939  94944  94949  94954  94959  94908  94968  94973  94978  94983 

4988  4993  4998  5002  5007  5012  5017  5022  5027  5032 

5036  5041  5046  5051  5056  5061  5066  5071  5075  5080 

5085  5090  5095  5100  5105  5109  5114  5119  5124  5129 

5134  5139  5143  5148  5153  5158  5163  5168  5173  5177 

5182  5187  5192  5197  5202  5207  5211  6216  5221  5226 

5231  5236  5240  5245  5250  5255  5260  5265  5270  5274 

5279  5284  5289  5294  5299  5303  5308  5313  6318  5323 

5328  5332  5337  5342  5347  5352  5357  5361  5366  5371 

5376  5381  6386  5390  5395  5400  5405  5410  5415  5419 

95424  95429  95434  95439  95444  95448  95453  95458  95463  95468 


TABLE  VI —LOGARITHMS  OF  NUMBERS.  5Q7 


N    0123456789 


900  95424  95429  95434  95439  95444  95448  95453  95458  95463  95468 

1  5472  5477  5482  5487  5492  5497  5501  6506  5511  5516 

2  6521  5525  5530  6535  5540  5545  5550  6554  5559  5564 

3  5569  5574  5578  5583  5588  5593  5598  5602  5607  5612 

4  5617  5622  5626  5631  5636  5641  5646  5650  6655  5660 

5  5665  5670  5674  5679  5684  5689  5694  6698  5703  5708 

6  6713  5718  5722  6727  5732  5737  6742  6746  6751  5756 

7  5761  6766  5770  6775  5780  6783  6789  6794  5799  5804 

8  5809  5813  5818  6823  6828  6832  5837  6842  5847  5852 

9  5856  5861  6866  6871  6875  6880  6885  5890  589$  6899 

910  95904  95909  95914  95918  95923  95928  95933  95938  95942  95947 

1  6952  5957  5961  6966  5971  5976  6980  5985  6990  699$ 

2  5999  6004  6009  6014  6019  6023  6028  6033  6038  6042 

3  6047  6052  6057  6061  6066  6071  6076  6080  6085  6090 

4  6095  6099  6104  6109  6114  6118  6123  6128  6133  6137 

5  6142  6147  6152  6156  6161  6166  6171  6175  6180  6185 

6  6190  6194  6199  6204  6209  6213  6218  6223  6227  6232 

7  6237  6242  6246  6251  6256  6261  6265  6270  627$  6280 

8  6284  6289  6294  6298  6303  6308  6313  6317  6322  6327 

9  6332  6336  6341  6346  6350  6355  6360  6365  6369  6374 

920  96379  96384  96388  96393  96398  96402  96407  96412  96417  96421 

1  6426  6431  6435  6440  6445  6450  6454  6459  6464  6468 

2  6473  6478  6483  6487  6492  6497  6501  6506  6511  6515 

3  6520  652$  6530  6534  6539  6544  6548  6553  6658  6562 

4  6567  6572  6577  6581  6586  6591  6595  6600  660$  6609 

5  6614  6619  6624  6628  6633  6638  6642  6647  6652  6656 

6  6661  6666  6670  6675  6680  668$  6689  6694  6699  6703 

7  6708  6713  6717  6722  6727  6731  6736  6741  6745  6750 

8  675$  6759  6764  6769  6774  6778  6783  6788  6792  6797 

9  6802  6806  6811  6816  6820  682$  6830  6834  6839  6844 

930  96848  96853  96858  96862  96867  96872  96876  96881  96886  96890 

1  689$  6900  6904  6909  6914  6918  6923  6928  6932  6937 

2  6942  6946  6951  6956  6960  696$  6970  6974  6979  6984 

3  6988  6993  6997  7002  7007  7011  7016  7021  7025  7030 

4  703$  7039  7044  7049  7053  7058  7063  7067  7072  7077 

5  7081  7086  7090  7095  7100  7104  7109  7114  7118  7123 

6  7128  7132  7137  7142  7146  7151  7155  7160  716$  7169 

7  7174  7179  7183  7188  7192  7197  7202  7206  7211  7216 

8  7220  7225  7230  7234  7239  7243  7248  7253  7257  7262 

9  7267  7271  7276  7280  7285  7290  7294  7299  7304  7308 

940  97313  97317  97322  97327  97331  97336  97340  97345  973$0  97354 

1  7359  7364  7368  7373  7377  7382  7387  7391  7396  7400 

2  7405  7410  7414  7419  7424  7428  7433  7437  7442  7447 

3  7451  7456  7460  746$  7470  7474  7479  7483  7488  7493 

4  7497  7502  7506  7511  7516  7520  7525  7529  7534  7539 

5  7543  7548  7552  7557  7562  7566  7571  7575  7580  7585 

6  7589  7594  7598  7603  7607  7612  7617  7621  7626  7630 

7  763$  7640  7644  7649  7653  7658  7663  7667  7672  7676 

8  7681  7685  7690  7695  7699  7704  7708  7713  7717  7722 
"9  7727  7731  7736  7740  774$  7749  7754  7759  7763  7768 

950  97772  97777  97782  97786  97791  97795  97800  97804  97809  97813 


508     TABLE  VI.— LOGARITHMS  OF  NUMBERS. 


950 
1 
2 

3 
4 
5 


9 

960 

1 
2 
3 
4 
5 
6 
7 


970 

1 
2 
3 
4 
5 
6 
7 
8 


980 
1 
2 
3 

4 
5 
6 

7 
8 


1 
2 
3 
4 
5 
G 
7 
8 
9 

1000 


97772  97777  97782  97786  97791  97795  97800  97804  97809  97813 

7818  7823  7827  7832  7836  7841  7845  7850  7855  7859 
7864  7868  7873  7877  7882  7886  7891  7896  7900  7905 
7909  7914  7918  7923  7928  7932  7937  7941  7946  7950 

7955  7959  7964  7968  7973  7978  7982  7987  7991  7996 

8000  8005  8009  8014  8019  8023  8028  8032  8037  8041 

8046  8050  8055  8059  8064  8008  8073  8078  8082  8087 

8091  8096  8100  8105  8109  8114  8118  8123  8127  8132 

8137  8141  8146  8150  8155  8159  8164  8168  8173  8177 

8182  8186  819X  8195  8200  8204  8209  8214  8218  8223 

98227  98232  98236  98241  98245  98250  98254  98259  98263  98268 

8272  8277  8281  8286  8290  8295  8299  8304  8308  8313 

8318  8322  8327  8331  8336  8340  8345  8349  8354  8358 

8363  8367  8372  8376  8381  8385  8390  8394  8399  8403 

8408  8412  8417  8421  8426  8430  8435  8439  8444  8448 

8453  8457  8462  8466  8471  8475  8480  8484  8489  8493 

8498  8502  8507  8511  8516  8520  8525  8529  8534  8538 

8543  8547  8552  8556  8561  8565  8570  8574  8579  8583 

8588  8592  8597  8601  8605  8610  8614  8619  8623  8628 

8632  8637  8641  8646  8650  8655  8659  8664  8668  8673 

98677  98682  98686  98691  98695  98700  98704  98709  98713  98717 

8722  8726  8731  8735  8740  8744  8749  8753  8758  8762 

8767  8771  8776  8780  8784  8789  8793  8798  8802  8807 

8811  8816-8820  8825  8829  8834  8838  8843  8847  8851 

8856  8860  8865  8869  8874  8878  8883  8887  8892  8896 

8900  8905  8909  8914  8918  8923  8927  8932  8936  8941 

8945  8949  8954  8958  8963  8967  8972  8976  8981  8985 

8989  8994  8998  9003  9007  9012  9016  9021  9025  9029 

9034  9038  9043  9047  9052  9056  9061  9065  9069  9074 

9078  9083  9087  9092  9096  9100  9105  9109  9114  9118 

99123  99127  99131  99136  99140  99145  99149  99154  99158  99162 

9167  9171  9176  9180  9185  9189  9193  9198  9202  9207 

9211  9216  9220  9224  9229  9233  9238  9242  9247  9251 

9255  9260  9264  9269  9273  9277  9282  9286  9291  9295 

9300  9304  9308  9313  9317  9322  9326  9330  9335  9339 

9344  9348  9352  9357  9361  9366  9370  9374  9379  9383 

9388  9392  9396  9401  9405  9410  9414  9419  9423  9427 

9432  9436  9441  9445  9449  9454  9458  9463  9467  9471 

9476  9480  9484  9489  9493  9498  9502  9506  9511  9515 

9520  9524  9528  9533  9537  9542  9546  9550  9555  9559 

99564  99568  99572  99577  99581  99585  99590  99594  99599  99603 

9607  9612  9616  9621  9625  9629  9634  9638  9642  9647 

9651  9656  9660  9664  9669  9673  9677  9682  9686  9691 

9695  9699  9704  9708  9712  9717  9721  9726  9730  9734 

9739  9743  9747  9752  9756  9760  9765  9769  9774  9778 

9782  9787  9791  9795  9800  9804  9808  9813  9817  9822 

9826  9830  9835  9839  9843  9848  9852  9856  9861  9865 

9870  9874  9878  9883  9887  9891  9896  9900  9904  9909 

9913  9917  9922  9926  9930  9935  9939  9944  9948  9952 

9957  9961  9965  9970  9974  9978  9983  9987  9991  9996 

00000  00004  00009  00013  00017  00022  00026  00030  00035  00039 


INDEX 


Abbott,  Dr.  Samuel  W.,  6,  235,      Averages,  49. 


239,  432. 
Abscissae,  67. 
Accident  statistics,  446. 
Accuracy,  26. 

of  state  censuses,  145. 
Adjusted,  and  gross  death-rates, 

246-249. 

death-rates,  240,  245. 
Adjustment  of  population,  131. 
Age,  census  meaning,  166. 

composition,    effect    on    death- 
rate,  231. 
distribution,  165. 
distribution   of   population,    in 

Europe,  182. 
distribution    of    population    in 

United  States,  182,  184. 
groups,  170. 

of  mother,  infant  mortality,  363. 
plotting,  73. 
unknown,  171. 
Ages  of  man,  221. 
American    Experience    Mortality 

Table,  426. 

Journal  of  Public  Health,  457. 
Public  Health  Association,  6. 
Analysis  of  death-rates,  299. 
Appeal  to  the  eye,  60. 
'    Arithmetical  increase,  131. 
!    Arithmetic  probability  paper,  395. 
Army  diseases,  440,  441. 
Array,  39,  41. 


Average  age  at  death,  374. 
age  of  persons  living,  372. 

Bacterial  counts,  26. 
Batt,  Dr.  W.  R.,  452. 
Ben  Day  system,  96. 
Bernouilli's  Theorem,  398. 
Bertillon,  Louis  A.,  6. 

Alphonse,  6. 

Jacques,  254. 
Binomial  theorem,  381. 
Biometrics,  2. 
Birth-rates,  195. 

Germany  and  England,  66. 

relation  to  death-rates,  195. 
Birth  registration,  109. 

advantages,  111. 

incomplete,  111. 

Births,  standard  certificate,  488. 
Blue  prints,  96. 

Bolduan,  Dr.  Charles  F.,  443,  454. 
Bones,  diseases  of,  265. 
Boston,  adjusted  death-rate,  245. 

age      distribution      of      infant 
deaths,  353. 

causes  of  infant  deaths,  356,  359, 
360. 

infant  mortality,  348. 

infant  mortality  by  age  periods, 
356. 

population  density,  152. 

specific  death-rates,  235. 


509 


510 


INDEX 


Boston,  stillbirths,  340. 

tuberculosis  death-rate,  80. 
Bowley,  correlation  studies,  412. 
Bowleys,  rulesf  orenumeration,  106. 
Brinton,  W.  C.,  59. 
Brockton,  analysis  of  death-rates, 
303. 

specific  death-rates,  305. 
Brooklyn,  typhoid  fever,  83. 
Burn,  Vital  Statistics  Explained, 
430. 

Cambridge,   adjusted  death-rate, 
244,  246. 

age  distribution  of  population, 
172,  175,  176. 

causes  of  death,  65 

deaths  distributed  by  age,  242. 

diphtheria,  320. 

incomplete    birth    registration, 
112. 

population,  138. 

population  density,  152. 

population  distributed  by  age, 
243. 

specific  death-rates,  233. 

tuberculosis  statistics,  313. 
Cancer,  specific  death-rates,  335. 

statistics,  334. 
Causal  relations,  402. 
Causality  and  correlation,  404. 
Causation,  laws  of,  405. 

and  correlation,  420. 
Causes  of  death,  254. 

infants,  356,  359,  360. 

international  list,  257. 
Census  date,  100. 

U.  S.,  100. 
Certificate  of  birth,  standard,  489. 

of  death,  standard,  490. 
Chadwick,  Edwin,  6. 


Chance,  379. 

element  in  sanitation,  394. 
natural  phenomena,  382. 
Chapin,  Dr.  Charles  V.,  323,  324, 

451. 

Charts,  93. 
Chicago,  Municipal  Tuberculosis 

Sanitorium,  413. 
Child  mortality,  346. 
Childhood,  early,  diseases,  369. 
mortality,  368. 
proportionate  mortality,  370. 
Children's  Bureau,  U.  S.  Dep't  of 

Labor,  361,  365. 

Children,  specific  death-rates,  369. 
Chronological  changes  in  death- 
rates,  234. 

changes  in  vital  rates,  210. 
Cincinnati,  population  estimates, 

140. 
Circulatory    system,   diseases  of, 

261. 

Cities,  rate  of  growth,  137. 
Civil  divisions,  103. 
Classes,  39,  40. 
Classification,  39. 

of  diseases  in  1850,  256. 
of  population,  161. 
Coefficient  of  variation,  388,  389. 
Coin  tossing,  379,  381. 
Collection  of  data,  17. 
Color  in  diagrams,  93. 
Component  part  diagrams,  95. 
Concealed  classification,  238. 
Conception   of   frequency    curve, 

399. 
Connecticut,  measles  and  grippe, 

410. 

Consumption  (see  Tuberculosis). 
Corrected  death-rates,  189,  239. 
Correlation,  402. 


INDEX 


511 


Correlation,  and  causality,  404. 

color  of  water  and  typhoid  fever, 
411. 

example,  410. 

Galton's  coefficient,  409. 

housing  and  tuberculosis,  413, 

methods,  407. 

mosquitoes  and  malaria,  419. 

secondary,  415. 

shown  graphically,  411. 

spurious,  416. 

table,  413,  415. 

use  by  epidemiologists,  418. 

vaccination  and  influenza,  420. 

water    nitration    and    typhoid 

fever,  416. 

Credibility  of  census,  106. 
Cross-section  paper,  87,  90. 
Cumulative  grouping,  48. 

plotting,  75. 
Curves,  equation  of,  98. 

Davis,  Dr.  W.  H.,  358. 
Death,  average  age,  374. 

certificate,  standard,  276,  490. 

registration,  uses  of,  115. 
Deaths,  registration  of,  113. 
Death-rates,  186. 

adjusted   to   standard   popula- 
tion, 240. 

analysis  of,  299. 

effect  of  size  of  place,  192. 

limited  use,  216. 

precision,  187. 

relations  to  birth-rates,  195. 
Deceptions,  graphical,  61. 
Demographers,  5. 
Demography,  science,  1. 

divisions,  2. 

influence  of  war,  442. 
Density  of  population;  150. 


Detroit,  population  of,  138. 
Deviation  from  mean,  385. 

standard,  387. 
Diagrams,  types  of,  59,  63. 
Digestive  system,  262. 
Diphtheria,  age  susceptibility,  323. 

fatality,  324. 

in  Cambridge,  320. 

in  Massachusetts,  325. 

in  Providence,  323,  324. 

urban  and  rural,  325. 
Divorce-rates,  200,  216. 
Double  coordinates,  81. 
Doubtful  observations,  391. 
Dry  statistics,  8. 
Dublin,  Dr.  Louis  I.,  Ill,  369. 
Dwellings,  number  of  persons  in, 
164. 

Earnings  of  father,   infant  mor- 
tality, 365,  366. 
Economic  conditions  and  health, 

445. 

Education,  infant  mortality,  363. 
Elderton,  correlation,  411. 
Endemic  index,  454. 

median,  454. 
Enforcement  of  registration  law, 

111. 
England,   vital  statistics  of,    12, 

210. 

Enumeration,  17,  100. 
Equation  of  curves,  98,  415. 
Error  of  statistics,  19. 
Error,  probable,  390. 
Errors  in  age,  167. 

in  published  death-rates,  192, 
in  round  numbers,  168. 
Estimates  of  population,  129,  137, 

139. 
Eugenics,  2. 


512 


INDEX 


Expectation  of  life,  428,  434. 

formulas  for,  430. 

infants,  355. 
External  causes  of  death,  266. 

Fallacy  of  concealed  classification, 

238. 
Families,  number  of  persons  in, 

164. 

Fair,  Dr.  William,  6,  254,  255. 
Fatality  rate,  309. 

of  diphtheria,  324. 

of  typhoid  fever,  330. 
Fecundity,  196. 

relation  to  age,  198. 
Feeding,  infant  mortality,  36-i 
Final  death-rate,  191. 
First-year  death-rate,  343. 
Fisher,  Arne,  430. 
France,  vital  statistics  of,  12,  210. 
Frequency  curve,  378. 

curve  as  a  conception,  399. 

natural,  376. 
Frankel,  Dr.  Lee  K.,  122. 

Galton,  Sir  Francis,  3,  5,  6. 
Galton's  coefficient  of  correlation, 

409. 

Garment  workers,  health  of,  446. 
Genealogy,  2. 
General  death-rates,  186. 

diseases,  257. 

vital  rates,  use  of,  204. 
Generalization,  39,  40. 
Genito-urinary    system,    diseases 

of,  262. 

Geometric  mean,  50. 
Geometrical  increase,  132,  133. 
Germany,  vital  rates,  210. 
Glover,  Prof.  James  W.,  433. 
Gonorrhoea  reportable,  120. 


Graphical  deceptions,  61. 

method  of  estimating  popula- 
tion, 141. 

Graphics,  statistical,  58. 

Graunt,  Capt.  John,  3,  4,  6. 

Great  war,  effect  on  demography, 
442. 

Gross  death-rates,  186. 

Group  designations,  45. 

Group  plotting,  71,  74. 

Grouping,  cumulative,  48. 
percentage,  47. 

Groups,  39,  40,  43. 

Guilfoy,  Dr.,  432. 

Gummed  letters,  94. 

Halley,  Edmund,  4. 

Hamburg,  infant  mortality,  341, 
343,  344,  353. 

Harmonic  mean,  52. 

Hazen's  theorem,  450. 

Health  officer,  use  of  statistics, 
11. 

Heights  of  soldiers,  377,  383,  395. 

Higher  ages,  proportionate  mor- 
tality, 372. 

Hoffman,  Dr.  F.  L.,  334,  338. 

Hollerith  punching  machine,  54. 

Holt,  Dr.  Wm.  L.,  245. 

Homes  and  infant  mortality,  361. 

Horizontal  scale,  69. 

Hospital  discharge  certificate,  471. 

Hospital  statistics,  443. 

Housing  and  tuberculosis,  413. 

Household  duties,  infant  mortal- 
ity, 364. 

Hungary,  vital  rates,  210. 

Ideal  death-rate,  216. 
Ill-defined  diseases,  267. 
Illegitimate  births,  198. 


INDEX 


513 


Immigration,  141,  142. 
Incompleteness  of  morbidity  sta- 
tistics, 119. 

Increase,  natural  rate  of,  203. 
Index,  31. 

of  concentration,   round  num- 
bers, 169. 
Induction,  14. 
Industrial  accidents,  446. 

classification,  280. 

statistics,  443. 
Inexact  numbers,  24,  26. 
Infancy,  diseases  of,  265. 
Infant  deaths,  age  distribution  in 
Boston,  353. 

causes,  Johnstown,  360. 
Infant  mortality,  339. 

age  of  mother,  363. 

age  periods,  355. 

and  homes,  361. 

birth  attendance,  362. 

Boston,  348. 

education,  363. 

father's  earnings,  365,  366. 

feeding,  364. 

foreign  cities,  350. 

household  duties,  364. 

methods  of  statement,  345. 

order  of  birth,  366. 

problems,  367. 

reasons  for  decrease,  349. 

sleeping  rooms,  362. 

Sweden,  345. 

U.  S.  cities,  351. 

ventilation,  362. 

Infants,  causes  of  death,  Boston, 
356. 

deaths  at  different  ages,  352. 
Infants,  definitions,  339. 

expectation  of  life,  355. 

life  tables,  354. 


Infants,  proportionate  mortality, 

344. 

specific  death-rates,  341. 
International  classification  of  dis- 
eases, 254. 

list  of  causes  of  death,  255,  257. 
Irregular  group  plotting,  72. 

Jarvis,  Edward,  6,  108. 
Jevons,  W.  Stanley,  10,  403. 
Johnson,  George  A.,  332. 
Johnstown,   first  year  mortality, 
344. 

stillbirths,  341. 

studies,  360,  361. 
Joint  causes  of  death,  270. 

Kensington,  birth-rates,  199. 
King,  404. 

Lag,  417,  418. 

Laplace,  probability  studies,  4. 
Lathrop,  Miss  Julia  C.,  361. 
Lead-poisoning,  444. 
Least  squares,  386. 
Lettering,  91,  92. 
Life-rates,  424. 
Life  tables,  422. 

based    on    living    populations, 
430. 

early  history,  431. 

infants,  354. 

recent,  431. 
Living  persons,  average  age,  372. 

median  age,  373. 
Local  death-rates,  190. 
Logarithmic  paper,  87. 

plotting,  85,  88. 
Logarithms,  34,  84. 

table  of,  491. 
Logic,  use  of,  9. 


514 


INDEX 


Lowell,   analysis   of   death-rates, 

303. 
specific  death-rates,  305. 

Malformations,  265. 
Malthus,  4. 
Maps,  statistical,  96. 
Marital  condition,  effect  on  death- 
rates,  229. 

Marriage-rates,  200,  215. 
Marriage  registration,  115. 
Massachusetts,    age   distribution, 
169. 

analysis  of  death-rates,  300. 

birth-rates,  212. 

causes  of  deaths,  310. 

causes  of  divorce,  201. 

death-rates,  1900-10,  212. 

death-rates  by  counties,  302. 

death-rates  of  cities,  303. 

death-rates  plotted,  396. 

diphtheria,  325. 

divorce-rates,  201,  216. 

errors  in  death-rates,  194. 

General  Hospital,  444. 

infant  mortality,  347. 

marriage-rates,  215. 

monthly  death-rates,  214. 

morbidity  registration,  116. 

population  estimates,  140. 

seasonal  mortality,  306. 

specific  death-rates,  236. 

tuberculosis   deaths   by   years, 
317. 

tuberculosis  death-rate,  79. 

variations  in  death-rates,  397. 

venereal  diseases,  120. 
Maternal  mortality,  367. 
Mechanical  computers,  53. 
Mechanics  of  diagrams,  89. 
Median,  42. 


Median  age  of  living  persons,  373. 
Medical  examiners,  278. 
Metropolitan  districts,  161. 
Military  statistics,  437. 
Mill,  John  Stuart,  406. 
Mills-Reincke,  phenomenon,  450. 
Mirza,  vision  of,  224. 
Misuse  of  rates,  30. 
Model    state    law,     births    and 
deaths,  472. 

state  law,  morbidity,  465. 
Monographic  method,  14. 
Monthly  death-rates,  214. 
Morbidity  registration,  116. 

model  law,  117. 

rate,  309. 

reports,  model  law,  465. 

standard  blank,  470. 
Mortality  rate,  308,  425. 
Moscow,  death-rates,  78. 
Most  probable  life-time,  427. 
Moving  average,  53. 

National  Health  Department,  128. 

statistics,  127. 

vital  statistics,  12. 
Nationality,  effect  on  death-rate, 

230. 

Natural  frequency,  376. 
Nervous  system,  diseases  of,  260. 
New  Jersey,  tuberculosis,  318. 
New  South  Wales,  226,  241. 
New  York  City,  maternal  mortal- 
ity, 367. 

life  tables,  432. 

resident  death-rates,  191. 
New  York,  tuberculosis,  320. 
Newsholme,  199. 
Nightingale,  Florence,  5,  6. 
Non-reportable  diseases,  120. 
Normalized  average,  454. 


INDEX 


515 


Nosography,  254. 
Nosology,  254. 

not  exact  science,  297. 
Notifiable  diseases,  118. 
Notification,  107. 

Occupation  and  tuberculosis,  318. 
Occupation,  index,  280. 
Occupations,  list  of,  281. 
Old  age,  diseases  of,  265. 
One  scale  diagrams,  64. 
Optical  illusions,  62. 
Ordinates,  67. 

Panics,    relation    to    birth-rates, 

213. 
Particular    diseases,    adjustments 

of  death-rates,  251. 
Pathometrics,  2. 
Pearson,  Karl,  3,  5,  224,  385. 
Percentage  grouping,  47. 

of  mortality,  308. 
Peddle's  Graphical  Charts,  98. 
,  Physical  examinations,  123. 
i  Physicians'  pocket  reference,  256. 
Plotting,  66,  70. 

paper,  90. 

Poates  Engraving  Company,  98. 
Polar  coordinates,  81. 
Poliomyelitis,  age  distribution,  48, 

448. 
Population,  129. 

age  distribution,  Europe,  182. 

estimates,  211. 

race,  color,  nativity,  etc.,  161. 

rate  of  increase,  136. 

redistributed  by  age,  172. 

types,  178. 

Powers'  statistical  machines,  54. 
Precision,  26. 
Precision  of  death-rates,  187. 


Preliminary  death-rate,  191. 
Prenatal  deaths,  340. 
Primary  cause  of  death,  278. 
Probability  of  living  a  year,  422. 
Probability  paper,  393,  398. 
Probability,  use  of,  398. 
Probability  scale,  391. 
Probable  error,  390. 
Progressive,  character  of  age  dis- 
tribution, 175. 

type  of  population,  178. 
Proportionate  mortality,  308. 

childhood,  370. 

higher  ages,  372. 

U.  S.,  95. 

Providence,  diphtheria,  323,  324. 
Puerperal  state,  diseases  of,  263, 

Quartiles,  42. 

Quetelet,  probability  studies,  5. 

Race  and  tuberculosis,  319. 

effect  on  death-rate,  234. 
Racial  adjustments  of  death-rates, 
249. 

composition  of  population,  162. 
Radial  plotting,  82. 
Rainfall  plotting,  68. 
Rates,  29,  32. 
Ratios,  27. 

Ratio  cross-section  paper,  83. 
Rectangular  coordinates,  66. 
Redistribution  of  population,  172, 

174. 

References,  459. 

Regressive  type  of  population,  178. 
Registrars,  laxity  of,  112. 
Registration,  17,  100,  107,  113. 

area  for  deaths,  123. 

area  for  births,  127. 

of  morbidity,  116. 


516 


INDEX 


Registration  of  marriages,  115. 
Registration,  model  law,  472. 
Reinhardt's  lettering,  91. 
Reports,  publication  of,  455. 
.  Reports,  standards,  457. 
Representative  method,  14. 
Reproduction  of  diagrams,  97. 
Resident,  death-rates,  190. 
Respiratory  system,  261. 
Restricted  death-rates,  220. 
Revised  death-rates,  192. 

estimates  of  population,  138. 
Richmond,  tuberculosis,  320. 
Rochester,  population  estimates, 

140. 

Round  numbers,  error  of,  168. 
Rural  and  urban  population,  146, 

149. 

Sanitary  index,  451. 

Saxelby's  mathematics,  98. 

Scales,  choice  of,  77. 

Schedules  of  enumeration,  103J 

School  age,  mortality  of  children, 
371. 

Seasonal,  deaths  from  tuberculo- 
sis, 315. 
distribution  of   typhoid   fever, 

331,  332. 
mortality,  306. 

Secondary  correlation,  415,  418. 

Sedgwick  and  MacNutt,  450. 

Senility,  265. 

Series,  39. 

Set-backs,  417. 

Sex  distribution,  163. 

Shattuck,  Lemuel,  108. 

Short  term  death-rates,  194. 

Sickness,  surveys,  122. 

Skew  curves,  383. 

Skin,  diseases  of,  264. 


Sleeping  rooms  and  infant  mor- 
tality, 362. 
Slide  rule,  35. 
Smith,  Adam,  4. 
Soldiers,    heights    of,    377,    383, 

395. 

Specific    death-rates,     220,     225, 
252. 

by  age  and  sex,  227. 

use  of,  239. 

U.  S.,  435. 

Specific  life-rates,  424. 
Springfield,    population  estimate, 

143. 

Spurious  correlation,  416. 
Standard,  birth  certificate,  109. 

certificates,  488,  490. 

certificate  of  death,  113,  276. 
Standardized  death-rates,  239. 

Standard,  deviation,  387. 

morbidity  blank,  470. 

million,  181. 
State  censuses,  145. 
States  in  registration  area,  125. 
State  sanitation,  108. 
Stationary    type    of    population, 

178. 
Statistical,  graphics,  58. 

induction,  14. 

maps,  96. 

method,  6,  14. 

processes,  17. 

units,  18. 

Statistics,  history  of,  3. 
Stillbirths,  195,  340. 
Summation  diagrams,  75,  385. 
Sundbarg,  12,  178. 
Sussmilch,  Peter,  4. 
Sweden,  age  distribution,  180. 

increase  in  population,  203. 

infant  mortality,  345. 


INDEX 


517 


Sweden,  progressive  age  distribu- 
tion, 177. 

vital  statistics  of,  12. 

vital  rates,  204. 
Syphilis  reportable,  120. 

Tabulation,  20. 
Tally  sheets,  20. 
Time  plotting,  69. 
Tuberculosis,  age  and  sex,  311. 

and  housing,  413. 

and  occupation,  318. 

and  race,  319. 

Boston,  80.  s 

death-rate,  79. 

proportionate  mortality,  316. 

N.  Y.  and  Richmond,  320. 

seasonal  distribution  of  deaths, 

315. 

Typhoid  fever,   age  distribution, 
47,  328. 

and  water  nitration,  333. 

Brooklyn,  83. 

case  fatality,  330. 

chronological  changes,  332. 

seasonal  changes,  331,  332. 

specific  death-rates  by  ages,  329. 

statistical  study,  327. 

synonyms,  275. 

Undesirable  terms  for  causes  of 

death,  271. 

Undertaker,  certificate,  114. 
United  States  army,  vital  statis- 
tics, 438,  439. 
cancer  statistics,  335. 
causes  of  death,  311. 
census,  100. 
cities,  increase  in  number,  149. 


United  States,  cities,  list  of  popu- 
lations, 154. 

life  tables,  429,  433,  434. 

population  plotted,  88. 

proportionate  mortality,  95. 

registration  area  of  births,  127. 

registration  area  for  deaths,  123. 

tuberculosis  statistics,  315. 

vital  statistics  of,  12. 
Units,  statistical,  18. 
Urban  and  rural  population,  146, 
149. 

Variation,  coefficient,  388,  389. 
Variations  in  death-rate,  192. 
Venereal  diseases,  reportable,  120. 
Ventilation,  infant  mortality,  362. 
Vie  probable,  427. 
Vision  of  Mirza,  224. 
Vital,  bookkeeping,  10. 

rates,     chronological     changes, 
210. 

statistics,  current  use,  452. 

Wall  charts,  93. 

War,  effect  on  demography,  442. 

Water  filtration,  and  typhoid  fever, 

333. 

Wax  process,  98. 
Wedding-rates,  200. 
Weighted  average,  50. 
Westergaard,  7,  404. 
Whipple,  George  C.,  108. 
Whitechapel,  birth-rates,  199. 
Willcox,  Walter  F.,  229,  334. 
Wright,  Carroll  D.,  6. 

Zinc  process,  97. 


Subjects  Related  to  this  Volume 

For  convenience  a  list  of  the  Wiley  Special  Subject  Catalogues, 
envelope  size,  has  been  printed.  These  are  arranged  in  groups 
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Canning  and  Preserving. 

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CHEMISTRY 

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Supply. 

(Over) 


CIVIL  ENGINEERING—  Continued 

5e  Highways;  Municipal  Engineering;  Sanitary  Engineering; 
Water  Supply.  Forestry.  Horticulture,  Botany  and 
Landscape  Gardening. 


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Power  and  Power  Plants;  Thermodynamics  and  Heat  Power. 
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12 — Medicine.  Pharmacy.  Medical  and  Pharmaceutical  Chem- 
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